Symbolic Data Analysis: Techniques for Qualitative Data Exploration
Introduction
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
Quantitative data analysis techniques have dominated the field of data science for decades.
However, not all types of data are numerical - many data sources contain qualitative,
categorical or mixed attribute information that defy traditional statistical methods. Symbolic
Data Analysis (SDA) provides techniques specifically designed for exploring qualitative and
mixed attribute data. This emerging field offers data scientists new tools to gain insights from
complex, non-standard datasets. This paper will introduce some of the key concepts and
methods in SDA and demonstrate their application using examples.
What is Symbolic Data?
Traditional quantitative data consists of atomic numerical values observed for each entity like
height, weight, test scores etc. In contrast, symbolic data contains information that is more
complex and possibly imprecise. Examples include:
- Sets or intervals instead of single values (e.g. income between $50,000-$75,000)
- Multiple simultaneous values for a categorical attribute (e.g. voting preferences across
parties)
- Relationships between attributes (e.g. correlated gene expressions)
- Hierarchies and taxonomies (e.g. product categorization tree)
- Concepts represented by text or images instead of simple variables
- Data objects themselves as the units of observation instead of atomic variables
In essence, symbolic objects contain summaries or descriptions of groups, concepts or
aggregates - not exact individual observations. They describe properties and relationships at a
higher abstraction level.
Symbolic Data Types
The main types of symbolic objects defined in SDA literature are:
- Symbolic Variables - Describe a value or set of values that an attribute may take (e.g.
income interval)
- Symbolic Relations - Multi-valued attributes to represent complex object properties (e.g. co-
occurring diagnoses)
- Symbolic Tuples - Composite objects made of other symbolic objects (e.g. customer
profile)
- Symbolic Concepts - Descriptions of general ideas represented by text/images rather than
variables
- Symbolic Time Series - For temporal data abstracted into intervals/concepts
- Symbolic Trees - To represent hierarchies and taxonomies of categories/concepts
- Symbolic Matrices - For relational datasets represented as matrices of variables
Choosing the right symbolic data type depends on the problem context and level of
abstraction needed. Multiple types can be used together in an analysis.
Symbolic Operators and Descriptive Statistics
Once data is represented symbolically, SDA extends traditional operators and descriptive
statistics to these complex objects:
- Set operators - Union, intersection, complement etc. to combine symbolic variables
- Aggregation - Medoids, intervals, histograms to summarize groups of objects
- Proximity/similarity measures - Overlap, matching, affinity indexes for symbolic relations
- Subgroup discovery - Finding characteristic patterns in object space
- Pattern mining - Extracting recurring symbolic concepts from textual attributes
- Outlier detection - Flagging unusual symbolic observations
- Hierarchical/taxonomy analysis - Measures to analyze symbolic tree structures
- Concept formation - Creating symbolic descriptions of clusters/groups
- Association rule mining - Finding correlations between symbolic variables
This allows mining insightful patterns, relationships and summaries that remain hidden at
atomic data levels. Symbolic modeling expands the toolkit for qualitative data exploration.
Example Analyses
Some examples demonstrate applying SDA to real datasets:
Customer profiling: Behavioral and demographic surveys contained intervals, sets. Clustering
on symbolic variables revealed complementary customer segments for targeted campaigns.
Education data: Student background/performance surveys contained multi-value academic
majors and career interests as symbolic variables. Association analysis revealed predictive
clusters for academic advising and program planning.
Healthcare records: Clinical notes represented as symbolic concepts linked to diagnoses.
Extracting frequent concept patterns identified characteristic syndromes and improved
diagnostic accuracy.
Social media analysis: Posts grouped by hashtags/topics formed symbolic documents. Graph-
based taxonomy discovery organized topics in a conceptual hierarchy followed by
influencers.
Product reviews: Sentiment ratings coupled with descriptive text formed symbolic rating
tuples. Outlier detection filtered problematic reviews while concept mining identified
attribute-specific sentiment drivers.
Census analysis: Income, education levels represented as intervals in census tract profiles
created symbolic objects. Proximity analysis detected gentrification trends over time in
symbolic space.
The examples showcase how SDA unveils useful insights from datasets that resist traditional
statistical techniques due to qualitative or mixed attribute types.
Challenges and Future Directions
While promising, some challenges remain for further developing SDA:
- Complex algorithms slow computation on large dataset sizes vs. nominal data methods
- Interpreting results from analyses on abstract symbolic objects can be non-trivial
- Defining optimal SDA representations is problem-specific vs. automated nominal encodings
- Interface of SDA outputs back into predictive machine learning pipelines is still maturing
- Standards need establishing around symbolic data formats, tools and platforms
- Theory integrating SDA with related non-standard data techniques like text mining is
limited
Addressing these through enhanced symbolic data structures, scalable algorithms,
integrations with distributed computing frameworks and benchmarking on real-world tasks
will expand SDA's potential. Future areas of opportunity also include:
- Graph-based SDA extending current approaches to networked symbolic data
- Causal and time series SDA handling dynamics, feedback and temporal evolution
- Explainable SDA providing justifications for discovered symbolic patterns and relationships
- Interactive SDA with human-in-the-loop discovery and sensemaking
- Benchmark datasets and competitions to spur methodological advancement
As non-standard data becomes increasingly prevalent, SDA promises to equip data scientists
with powerful new lenses for exploration and storytelling from qualitative sources.
Conclusion
In conclusion, Symbolic Data Analysis introduces techniques specifically designed to
leverage the information inherent in qualitative, mixed attribute and complex datasets that
cannot be adequately described at nominal atomic variable levels. By representing and
operating on data at higher levels of abstraction, SDA uncovers patterns, relationships and
profiles that remain obscure otherwise. While still an emerging field, successful applications
show its potential for gaining insights across domains from social sciences to health,
marketing and beyond. Addressing current methodological challenges promises to further
expand this paradigm's impact on improving our understanding of humanity through non-
standard data exploration.
