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In: Data Mining ISBN: 978-1-63463-738-1

Editor: Harold L. Capri © 2015 Nova Science Publishers, Inc.

Chapter 3

MODELING NATIONS’ FAILURE VIA DATA

MINING TECHNIQUES

Mohamed M. Mostafa, Ph.D. Gulf University for Science and Technology, Kuwait

ABSTRACT

Since the concept of ‘failed states’ was coined in the early 1990s, it

has come to occupy a top tier position in the international peace and

security’s agenda. This study uses data mining techniques to examine the

effect of various social, economic and political factors on states’ failure at

the global level. Data mining techniques use a broad family of

computationally intensive methods that include decision trees, neural

networks, rule induction, machine learning and graphic visualization.

Three artificial neural network models: multi-layer perceptron neural

network (MLP), radial basis function neural network (RBFNN) and self-

organizing maps neural network (SOM) and one machine learning

technique (support vector machines [SVM]) are compared to a standard

statistical method (linear discriminant analysis (LDA). The variable sets

considered are demographic pressures, movement of refugees, group

paranoia, human flight, regional economic development, economic

decline, delegitimization of the state, public services’ performance,

human rights status, security apparatus, elites’ behavior and the role

played by other states or external political actors. The study shows how it

is possible to identify various dimensions of states’ failure by uncovering

complex patterns in the dataset, and also shows the classification abilities

of data mining techniques.

C o p y r i g h t 2 0 1 4 . N o v a S c i e n c e P u b l i s h e r s , I n c .

A l l r i g h t s r e s e r v e d . M a y n o t b e r e p r o d u c e d i n a n y f o r m w i t h o u t p e r m i s s i o n f r o m t h e p u b l i s h e r , e x c e p t f a i r u s e s p e r m i t t e d u n d e r U . S . o r a p p l i c a b l e c o p y r i g h t l a w .

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Mohamed M. Mostafa 54

Keywords: Failed states, neural networks, machine learning, computational

intelligence

1. INTRODUCTION AND LITERATURE SURVEY

Helman and Ratner (1993) defined failed states as those states that are

simply unable to function as independent entities. Helman and Ratner’s

classification included nations such as Haiti, Yugoslavia, the USSR, Sudan,

Liberia, and Cambodia. Zartman (1995) defined failed states as those in which

“the basic functions of the state are no longer performed” (p. 2). Zartman’s

classification included nations such as Congo of the 1960s; Chad, Ghana and

Uganda of the early 1980s; and Somalia, Liberia and Ethiopia of the early

1990s. Hehir (2007) argues that failed states suffer from both “coercive

incapacity” represented by monopolizing the use of force by the state and

“administrative incapacity” which involves a failure to provide the basic

services that most citizens expect from modern governments, such as a certain

level of personal security, economic stability, and functioning bureaucratic and

judicial systems. Using a multinomial logit model, Howard (2008) found that

the transition to a failing state is positively influenced by the presence of a

strong autocratic regime, state corruption and economic insecurity. However,

Lambach (2004) argues that there is no fine line between state failure and non-

failure. The author rather distinguishes between weak states that may still be

able to provide some level of political goods and collapsed states that cannot

guarantee even a modicum of order.

The 9/11 attacks brought failed states to the top tier of international peace

and security’s agenda. Afghanistan’s failure to combat Al-Qaeda has lent a

new attention to the concept because failed states were seen as safe harbors

and launching pads for terrorism and terrorist organizations. For example, in a

recent empirical study, Piazza (2008) found that the Failed States Index is a

significant predictor of transnational terrorism. Using a series of negative

binomial regressions, the author also found that states plagued by chronic state

failures are statistically more likely to host terrorist groups and are more likely

to be targeted by transnational terrorists themselves.

Although the failed states concept has emerged as a testable concept

almost 20 years ago, no previous studies have attempted to use computational

intelligence techniques to predict, classify and cluster failed nations and

nations with high political risk. In this research we aim to fill this research gap

by predicting, classifying and clustering state failure across 177 nations

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Modeling Nations’ Failure via Data Mining Techniques 55

through the use of intelligent modeling techniques. More specifically, the

purpose of this research is twofold:

 To determine the major factors that affect the state failure at the

global level; and

 To benchmark the performance of computational intelligence models

against traditional statistical techniques.

Thus, this paper makes at least two important contributions to the broader

literature on state failure. First, most previous studies devoted to understand

the state failure phenomenon are comprised of case study evaluations of few

failed states (e.g., Lemarchand, 2003; Reno, 2003). Our study includes 177

nations, which makes it the most comprehensive study so far. By doing so the

study adds depth to the knowledge base on state failure. Second, by employing

computational intelligence methods such as neural networks and support

vector machines, the study adds breadth to the debate over the causes of state

failure at the global level. The paper is organized as follows. The next section

summarizes the methodology used to conduct the analysis. The subsequent

section presents empirical results of the analysis. Next, the paper sets out some

implications of the analysis. This section also deals with the research

limitations and explores avenues for future research.

2. METHOD

2.1. Multi-Layer Perceptron

MLP consists of sensory units that make up the input layer, one or more

hidden layers of processing units (perceptrons), and one output layer of

processing units (perceptrons). The MLP performs a functional mapping from

the input space to the output space. The output of an MLP is compared to a

target output and an error is calculated. This error is back-propagated to the

neural network and used to adjust the weights. This process aims at

minimizing the mean square error between the network’s prediction output and

the target output.

One of the first successful applications of MLP is reported by Lapedes and

Farber (1988). Using two deterministic chaotic time series generated by the

logistic map and the Glass-Mackey equation, they designed an MLP that can

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Mohamed M. Mostafa 56

accurately mimic and predict such dynamic nonlinear systems. There is an

extensive literature in financial applications of MLP (e. g. Kumar and

Bhattacharya, 2006; Harvey et al., 2000). Another major application of MLP is

in electric load consumption (e.g., Darbellay and Slama, 2000; McMenamin

and Monforte, 1998). Many other problems have been solved by MLP. A short

list includes air pollution forecasting (e.g., Videnova et al., 2006), maritime

traffic forecasting (Mostafa, 2009), airline passenger traffic forecasting (Nam

and Yi., 1997), railway traffic forecasting (Zhuo et al., 2007), commodity

prices (Kohzadi et al., 1996), ozone level (Ruiz-Suarez et at., 1995), student

grade point averages (Gorr et al., 1994), forecasting macroeconomic data

(Aminian et al., 2006), advertising (Poh et at., 1998), and market trends (Aiken

and Bsat, 1999).

The MLP is the most frequently used neural network technique in pattern

recognition (Bishop, 2006) and classification problems (Sharda, 1994).

However, numerous researchers document the disadvantages of the MLP

approach. For example, Calderon and Cheh (2002) argue that the standard

MLP network is subject to problems of local minima. Swicegood and Clark

(2001) claim that there is no formal method of deriving a MLP network

configuration for a given classification task. Thus, there is no direct method of

finding the ultimate structure for modeling process. Consequently, the refining

process can be lengthy, accomplished by iterative testing of various

architectural parameters and keeping only the most successful structures.

Wang (1995) argues that standard MLP provides unpredictable solutions in

terms of classifying statistical data.

2.2. Radial Basis Function Neural Network

The basic architecture for a RBFNN is a 3-layer network. The input layer

is simply a fan-out layer and does no processing. The second or hidden layer

performs a non-linear mapping from the input space into a higher dimensional

space in which the patterns become linearly separable. The final layer

therefore performs a simple weighted sum with a linear output.

The unique feature of the RBFNN is the process performed in the hidden

layer. The idea is that the patterns in the input space form clusters. If the

centers of these clusters are known, then the distance from the cluster centre

can be measured. Furthermore, this distance measure is made non-linear, so

that if a pattern is in an area that is close to a cluster centre it gives a value

close to 1. Beyond this area, the value drops dramatically. The notion is that

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Modeling Nations’ Failure via Data Mining Techniques 57

this area is radially symmetrical around the cluster centre, so that the non-

linear function becomes known as the radial-basis function.

Since the RBFNN has only one hidden layer and has fast convergence

speed, it is widely used for non-linear mappings between inputs and outputs.

Examples include detecting spam email (Jiang, 2007), financial distress

prediction (Cheng et al., 2006), public transportation (Celikoglu & Cigizoglu,

2007), classification of active components in traditional medicine (Liu et al.,

2009), classification of audio signals (Dhanalakshmi et al., 2009), prediction

of athletes performance (Iyer & Sharda, 2009), and face recognition

(Balasubramanian et al., 2009).

2.3. Support Vector Machines

SVMs have been developed by Vapnik (1995) as a novel type of machine

learning. SVMs are a set of related supervised learning methods used for

classification and regression. In the case of classification, SVMs obtain the

‘optimal’ boundary of two classes in a vector space independently on the

probabilistic distributions of training vectors in the data set. If the categories

are linearly separated, the aim of SVMs is to find the ‘optimal’ hyperplane

boundary which separates both classes, classifying not only the training set but

also unknown samples. When the classes are non-linearly separable, the input

data are implicitly mapped into a higher dimensional space by a kernel

function, e.g., Guassian radial basis function (Berrueta et al., 2007).

SVMs are based on the structure risk minimization (SRM) principle,

which has been shown to be superior to the traditional risk minimization

(ERM) principle employed by neural networks (Kecman, 2005). SRM

minimizes an upper bound of the generalization error on the Vapnik-

Chernoverkis (VC) dimension, as opposed to ERM, which minimizes the

training error. Recently, Li et al., (2008) found that SVMs have better

modeling performance than the MLP in short-term freeway traffic volume

forecasting. Compared to neural networks, other SVMs advantages include

their strong theoretical basis which provides them with high generalization

capability. SVMs always have a solution, which can be quickly obtained by a

standard quadratic programming algorithm.

SVMs have been used in a range of areas like financial applications (e.g.,

Ravi et al., 2008), classification of fragrance properties (Luan et al., 2008),

dynamic classification for video stream (Awad & Motai, 2008), classification

of forest fire types (Koetz et al., 2008), consumer churn prediction

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Mohamed M. Mostafa 58

(Coussement and Van den Poel, 2008), text categorization (Hmeidi et al.,

2008), spam classification (Yu & Xu, 2008) and estimating production levels

(Chen & Wang, 2007).

2.4. Self-Organizing Maps

The SOM, also called Kohonen map, is a heuristic model for exploring

and visualizing patterns in high dimensional datasets. It was first introduced to

the neural networks community by Kohonen (1982). SOM can be viewed as a

clustering technique that identifies clusters in a dataset without the rigid

assumptions of linearity or normality of more traditional statistical techniques.

Indeed, like k-means, it clusters data based on an unsupervised competitive

algorithm where each cluster has a fixed coordinate in a topological map

(Audrain-Pontevia, 2006). The SOM is trained based on an unsupervised

training algorithm where no target output is provided and the network evolves

until convergence. Based on the Gladyshev’s theorem, it has been shown that

SOM models have almost sure convergence (Lo & Bavarian, 1993).

The SOM consists of only two layers: the input layer which classifies data

according to their similarity, and the output layer of radial neurons arranged in

a two-dimensional map. Output neurons will self-organize to an ordered map

and neurons with similar weights are placed together. They are connected to

adjacent neurons by a neighborhood relation, dictating the topology of the map

(Moreno et al., 2006). The number of neurons can vary from a few dozen to

several thousand. Since the SOM compresses information while preserving the

most important topological and metrical relationships of the primary data

elements on the display, it can also be used for pattern classification (Silven et

al., 2003).

Due to the unsupervised character of their learning algorithm and the

excellent visualization ability, SOMs have been recently used in myriad

classification and clustering tasks. Examples include classifying cognitive

performance in schizophrenic patients and healthy individuals (Silver &

Shmoish, 2008), mutual funds classification (Moreno et al., 2006), speech

quality assessment (Mahdi, 2006), vehicle routing (Ghaziri & Osman, 2006),

network intrusion detection (Zhong et al., 2007), anomalous behavior in

communication networks (Frota et al., 2007), compounds pattern recognition

(Yan, 2006), market segmentation (Kuo et al., 2002), clustering green

consumer behavior (Mostafa, 2009) and classifying magnetic resonance brain

images (Chaplot et al., 2006).

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Modeling Nations’ Failure via Data Mining Techniques 59

3. RESULTS

3.1. Preliminary Data Analysis

Failed states data in this study were taken from the Fund for Peace

(FundForPeace.org) and Foreign Policy magazine (2009). The failed states

index (FSI) rates 12 social, economic and political indicators, derived from

open-source materials. These 12 indicators are: mounting demographic

pressures, massive movement of refugees and internally displaced persons,

legacy of vengeance-seeking group grievance, chronic and sustained human

flight, uneven economic development along group lines, sharp or severe

economic decline, criminalization or de-ligitimazation of the state, progressive

deterioration of public services, widespread violation of human rights, security

apparatus as “state within state’”, rise of factionalized elites, and intervention

of other states or external actors. The rank order of the states shown in Figure

1 is based on the total scores of the 12 indicators. For each indicator, the

ratings are placed on a scale of 0 to 10, with 0 being the lowest intensity (most

stable) and 10 being the highest intensity (least stable). The total score is the

sum of the 12 indicators and is on a scale of 0-120. In the 2009 index there are

177 states, compared to only 146 in 2006 and 75 in 2005. Only recognized

sovereign states based on the UN membership are included in the analysis.

Thus, several territories such as Taiwan, Palestine and Kosovo are excluded

from the index. In 2009 the FSI ranged from 18.3 in Norway to 114.7 in

Somalia. Furthermore, the Fund for Peace places nations into four categories

based on their scores. The most at-risk countries are placed in the “Alert”

category. This group includes nations having indices between 91 and 120; the

“Warning” category is reserved for countries scoring between 61 and 90; the

“Monitoring” category includes nations with a score ranging from 31 to 60;

and the “Sustainable” category includes nations scoring between 12 and 30.

Figure 2 shows boxplots for all variables used in the analysis.

Since the FSI is supposed to measure states “failure” dimension, factor

analysis was conducted to ascertain the unidimensionality of the index. Using

a standard eigenvalue of 1.0 (Child, 1990) and an inspection of a scree plot

(Figure 3), factor analysis yielded one factor. Total variance explained (79.06

percent) exceeds the 60 percent threshold commonly used in social sciences to

establish satisfaction with the solution (Hair et al., 1998). We used the Kaiser-

Mayer-Olkin (KMO) measure of sampling adequacy (Kaiser, 1970) to

measure the adequacy of the sample for extraction of the three factors.

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Mohamed M. Mostafa 60

Alert Warning Monitoring/stable Sustainable/most stable No Information / Dependent

Territory.

Figure 1. Failed States Index. Sources: The Fund for Peace (FundForPeace.org) and

Foreign Policy (July/August, 2009, pp. 80-83).

Figure 2. Boxplots of variables used in the analysis.

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Modeling Nations’ Failure via Data Mining Techniques 61

The KMO value found (0.942) is indicative of a data set considered to be

highly desirable for factor analysis (Kim and Mueller, 1978). The Bartlett’s

test of sphericity, which tests whether the correlation matrix is an identity

matrix, is significant (Approx. Chi-square=3055.735, df=66, p<0.001). This

indicates the factor model is appropriate.

Figure 3. Scree plot of eigenvalues vs. components.

3.2. MLP, RBFNN and SVM-Based Classification

There are many software packages available for analyzing MLP models.

We chose SPSS Neural Networks (SPSS, 2007) package. This software

package applies artificial intelligence techniques to automatically find the

efficient MLP architecture (MLP design used in this study is shown in Figure

4). Typically, the application of MLP requires a training data set and a testing

data set (Lek and Guegan, 1999). The training data set is used to train the MLP

and must have enough examples of data to be representative for the overall

problem. The testing data set should be independent of the training set and is

used to assess the classification accuracy of the MLP after training. Following

Lim and Kirikoshi (2005), an error back-propagation algorithm with weight

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Mohamed M. Mostafa 62

updates occurring after each epoch was used for MLP training. The learning

rate was set at 0.1. Table 1 reports the properties of the MLP model. Table 2

shows the MLP classification accuracy. From table 2 we see that the MLP

classifier predicted training sample with 97.2% accuracy and validation

sample with 94.4% accuracy.

Figure 4. Multi-layer perceptron neural network architecture.

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Modeling Nations’ Failure via Data Mining Techniques 63

Table 1. MLP neural network configuration

Input

Layer

Covariates 1 Demog

2 Refugees

3 Grp_Griev

4 Hum_Flight

5 Uneven_Dev

6 Econ_Dec

7 State_Deleg

8 Pub_Serv

9 Hum_Rights

10 Sec_App

11 Fact_Elites

12 Exter_Interv

Number of Units a 12

Rescaling Method for Covariates Standardized

Hidden

Layer(s)

Number of Hidden Layers 1

Number of Units in Hidden Layer 1 a 5

Activation Function Hyperbolic tangent

Output

Layer

Dependent Variables 1 Failed_Status

Number of Units 4

Activation Function Softmax

Error Function Cross-entropy

a. Excluding the bias unit.

Table 2. MLP neural network classification

Sample Observed

Predicted

bdrline critical in_dang stable Percent Correct

Training bdrline 27 0 2 0 93.1%

critical 0 34 0 0 100.0%

in_dang 0 1 65 0 98.5%

stable 1 0 0 11 91.7%

Overall Percent 19.9% 24.8% 47.5% 7.8% 97.2%

Testing bdrline 3 0 0 1 75.0%

critical 0 4 0 0 100.0%

in_dang 1 0 26 0 96.3%

stable 0 0 0 1 100.0%

Overall Percent 11.1% 11.1% 72.2% 5.6% 94.4%

Dependent Variable: Failed_Status.

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Mohamed M. Mostafa 64

RBFNN was also implemented using the SPSS Neural Networks (SPSS,

2007) package (RBFNN design used in this study is shown in Figure 5). The

basic configuration of the RBFNN used is shown in Table 3. The learning

rates for the RBFNN parameters are varied between 0.001 and 0.1 and that for

the weights are varied between 0.1 and 0.7. The training is stopped if either the

error goal reaches 0.001 or if the maximum misclassification becomes lower

than one percent. Table 4 provides the basic RBFNN properties. From table 4

we see that the hit ratio for the training sample is 97.9% and the hit ratio for

the validation sample is 97%.

Figure 5. Radial basis function neural network architecture.

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Modeling Nations’ Failure via Data Mining Techniques 65

Table 3. RBF neural network configuration

Input

Layer

Covariates 1 Demog

2 Refugees

3 Grp_Griev

4 Hum_Flight

5 Uneven_Dev

6 Econ_Dec

7 State_Deleg

8 Pub_Serv

9 Hum_Rights

10 Sec_App

11 Fact_Elites

12 Exter_Interv

Number of Units 12

Rescaling Method for Covariates Standardized

Hidden

Layer

Number of Units 4 a

Activation Function Softmax

Output

Layer

Dependent Variables 1 Failed_Status

Number of Units 4

Activation Function Identity

Error Function Sum of Squares

a. Determined by the testing data criterion: The "best" number of hidden units is the

one that yields the smallest error in the testing data.

Table 4. RBF neural network classification

Sample Observed

Predicted

bdrline critical in_dang stable Percent Correct

Training bdrline 26 0 0 0 100.0%

critical 0 28 1 0 96.6%

in_dang 0 1 76 0 98.7%

stable 1 0 0 11 91.7%

Overall Percent 18.8% 20.1% 53.5% 7.6% 97.9%

Testing bdrline 7 0 0 0 100.0%

critical 0 9 0 0 100.0%

in_dang 1 0 15 0 93.8%

stable 0 0 0 1 100.0%

Overall Percent 24.2% 27.3% 45.5% 3.0% 97.0%

Dependent Variable: Failed_Status.

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Mohamed M. Mostafa 66

SVMs were implemented using the SVM function in R software

(Dimitradou et al., 2005). This function provides a user-friendly interface to

the LIBSVM software developed by Chang and Lin (2001) along with

visualization and parameter tuning methods. This function is currently one of

the most widely used implementations of SVM algorithms as it provides a

robust and fast SVM implementation and produces state of the art results on

most classification and regression problems (Karatzoglou et al., 2005).

Appendix A provides the R code used to conduct the SVM analysis. As seen

in Figure 6, the correct classification rate for both training and test samples

was 100%.

Figure 7 shows a contour plot of SVM performance at different levels of

complexity.

Figure 6. Support vector machine model complexity vs. error rate.

SVM model complexity

E rr

o r

ra te

1 2 3 4 5 6

0 3

6 9

1 2

1 6

2 0

2 4

2 8

3 2

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Modeling Nations’ Failure via Data Mining Techniques 67

Figure 7. Contour plot of SVM performance.

To study the effectiveness of MLP, RBFNN and SVM-based classification

of failed states, the results of MLP RBFNN and SVM were compared with the

traditional multiple discriminant analysis (MDA). MDA is frequently used

supervised pattern recognition technique. A linear function of the variables is

sought, which maximizes the ratio of between-class variance and minimizes

the ratio of within-class variance. MDA is an extremely simple and efficient

method of classification. Indeed, it cannot be outperformed if the two

distributions are normal and have the same dispersion matrix (i.e., Bayes

limit). Figure 8 shows the canonical discriminant functions’ failed states group

centroids. A common measure of predictive models is the percentage of

observation correctly classified or the hit ratio. The MDA model had an

accuracy rate of 93.2%, with a leave-one-out validation accuracy of 86.4% as

shown in Table 5.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0

20

40

60

80

100

Performance of `svm'

log10

C

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Mohamed M. Mostafa 68

Table 5. LDA classification results b,c

Failed_Code

Predicted Group

Membership

Total 1.0 2.0 3.0 4.0

Original Count 1.0 38 0 0 0 38

2.0 6 85 2 0 93

3.0 0 1 29 3 33

4.0 0 0 0 13 13

% 1.0 100.0 .0 .0 .0 100.0

2.0 6.5 91.4 2.2 .0 100.0

3.0 .0 3.0 87.9 9.1 100.0

4.0 .0 .0 .0 100.0 100.0

Cross-validated a Count 1.0 38 0 0 0 38

2.0 9 81 3 0 93

3.0 0 3 22 8 33

4.0 0 0 1 12 13

% 1.0 100.0 .0 .0 .0 100.0

2.0 9.7 87.1 3.2 .0 100.0

3.0 .0 9.1 66.7 24.2 100.0

4.0 .0 .0 7.7 92.3 100.0

a. Cross validation is done only for those cases in the analysis. In cross validation, each

case is classified by the functions derived from all cases other than that case.

b. 93.2% of original grouped cases correctly classified.

c. 86.4% of cross-validated grouped cases correctly classified.

Figure 9 displays the MLP cumulative gain chart (similar figure was

obtained for RBFNN). This chart shows the percentage of the overall number

of cases in a given category gained by targeting a percentage of the total

number of cases. For example, the first point on the curve for the in danger

category is at (10%, 20%), meaning that if a dataset is scored with the network

and all the cases are sorted by predicted pseudo-probability of donor, we

would expect the top 10% to contain approximately 20% of all of the cases

that actually take the category in danger. Likewise, the top 20% would contain

approximately 40% of in danger states, and so on.

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Modeling Nations’ Failure via Data Mining Techniques 69

Figure 8. Failed states group centroids.

Figure 9. Multi-layer perceptron neural network gain chart.

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Mohamed M. Mostafa 70

The diagonal line is the baseline curve; if 10% of the cases are selected

from the scored dataset at random, we would expect to gain approximately

10% of all of the cases that actually take the category donor. The farther above

the baseline a curve lies, the greater the gain.

Despite the satisfactory classification performance of the MLP, RBFNN

and SVM in this study, such models are often criticized as black boxes that do

not allow decision-makers to make inferences on how the input variables

affect the models’ results. One way to address this issue is to conduct a

variable impact analysis (VIA). The purpose of VIA is to measure the

sensitivity of net predictions to changes in independent variables. Figure 10

shows that the most important input variables for the MLP are refugees,

security apparatus and external intervention. Similar results were obtained

using the RBFNN. The lower the percent value for a given variable, the less

that variable affects the predictions. The results of the analysis can help in the

selection of a new set of independent variables, one that will allow more

accurate predictions. For example, a variable with a low impact value can be

eliminated in favor of some new variables.

Figure 10. Multi-layer perceptron neural network variable impact analysis.

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Modeling Nations’ Failure via Data Mining Techniques 71

3.3. SOM-Based Clustering

There are many software packages available for analyzing SOM models.

We chose SOMine package version 5.0 (Viscovery software, 2008). This

software applies artificial intelligence techniques to automatically find the

efficient SOM clusters. To visualize the cluster structure, some authors use the

unified distance matrix (U-matrix) (e.g., Vijayakumar et al., 2007; Stavrou et

al., 2010). However, this method does not give crisp boundaries to the clusters

(Worner & Gevrey, 2006). In this study a hierarchical cluster analysis with a

Ward linkage method was applied to the SOM to clearly delineate the edges of

each cluster. The number of neurons is chosen to be 2000. There are two

learning algorithms for SOM (Kohonen, 2001): the sequential or stochastic

learning algorithm and the batch learning algorithm. In the former, the

reference vectors are updated immediately after a single input vector is

presented. In the latter, the update is done using all input vectors. While the

batch algorithm does not suffer from convergence problems, the sequential

algorithm is stochastic in nature and is less likely trapped to a local minimum.

Following Ding & Patra (2007), we choose the sequential learning algorithm

to train the SOM.

The SOM cluster results are shown in Figure 11. This two-dimensional

hexagonal grid shows clear division of the input pattern into four clusters.

Since the order on the grid reflects the neighborhood within the data, features

of the data distribution can be read off from the emerging landscape on the

grid. Figure 11 shows four discernable clusters of failed states. This four-

cluster solution meets Siew et al., (2002) qualitative criteria that should be

used to select the representative SOM model. These criteria include

representability, explainability and level of sophistication. representability

refers to the fact that the variables in each cluster should be distinct and carry

some information of their own. This means that the resulting profile for each

cluster should be unique and meaningful. Explainability means that the

clusters themselves are distinct. Level of sophistication means that the size of

each cluster should be monitored so that there are no either too large clusters

that might hide more distinct groups in the cluster, or too small clusters that

might be an indication of artificial clusters.

When assessing the quality of clustering model for validation purposes,

quantitative criteria can also be used (Zhuang et al., 2009). We used the

Kohonen software package (Wehrens and Buydens, 2007) to validate the

cluster results.

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Mohamed M. Mostafa 72

Figure 11. SOM-Ward clusters.

Figure 12. SOM counts and quality plots.

Figure 12 shows both the SOM counts and the mapping quality. In the left

plot, the background color of a unit corresponds to the number of samples

mapped to the unit. This figure shows that there is a reasonable spread out

over the map. One of the units is empty (depicted in grey), which suggests that

no samples have been mapped to it. The right plot shows the quality of the

mapping. It represents the mean distance between objects mapped to a

particular unit and the input vector of that unit. A good mapping should show

small distances everywhere in the map. An alternative method, called the bi-

directional Kohonen mapping (Melssen et al., 2006) has also been

critical

in danger

border line

stable

Failed states data: counts

2

4

6

8

10

12

Failed states data: quality

1

2

3

4

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Modeling Nations’ Failure via Data Mining Techniques 73

implemented. Results obtained are very similar to the ones obtained above.

Another method to check the validity of the SOM during the training phase is

to see whether the input vectors are becoming more and more similar to the

closest objects in the dataset. Based on Figure 13 we see the effect of the

neighborhood shrinking to include only the winning unit. This implies that

there is no need for more iterations to optimize training parameters.

Figure 13. SOM neighborhood shrinkage plot.

Cluster 1 is called “critical.” This is the green-colored cluster with a

frequency of 21.47%. This cluster corresponds to the “alert.” zone in the Fund

for Peace classification. Cluster 2 is called “in danger.” This blue-colored

cluster has a frequency of 37.58%. This is the largest cluster and corresponds

to the “warning” zone in the Fund for Peace classification. The third cluster is

called “border line.” This yellow-colored cluster has a frequency of 20.34%.

This cluster corresponds to the “monitoring” zone in the Fund for Peace

0 20 40 60 80 100

0 .0

0 0

.0 1

0 .0

2 0

.0 3

0 .0

4 0

.0 5

Training progress

Iteration

M e

a n

d is

ta n

c e

t o

c lo

s e

s t u

n it

0 0

.0 0

5 0

.0 1

0 .0

1 5

0 .0

2

X

Y

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Mohamed M. Mostafa 74

classification. Finally, the fourth cluster is labeled “stable.” This cluster

corresponds to the “sustainable” zone in the Fund for Peace classification

Table 6 summarizes the basic information in each cluster. The SOM results

validate the Fund for Peace and Foreign Policy classifications.

Based on the SOM-Ward clusters, feature or component maps can be

constructed (Vesanto, 1999). These maps are also known in the literature as

‘temperature maps.’ (Churilov & Flitman, 2006). On these maps, the nodes

which share similar information are organized in close color proximity to each

other. Figure 14 shows the feature maps for every cluster and for all input

attributes. Feature maps show the distribution of values of the respective input

component over the map. Relationships between variables could be inspected

by visually comparing the pattern of shaded pixels for each map; similarity of

the patterns indicates strong monotonic relationships between the variables.

The name of the displayed input component appears on top of each map. The

color scale at the bottom of the component window shows that blue is used for

low values, green for mid-range values and red for high values. From the

feature maps we note, for example, that the “critical” cluster includes the

highest constellation of red pixels for nations characterized by mounting

demographic pressures, massive movement of refugees, group paranoia,

chronic or sustained human flight, uneven economic development, sharp

economic decline, delegitimization of the state, progressive deterioration of

public services, widespread violation of human rights, strong security

apparatus, factionalized elites and intervention of other states or external

political actors. This implies that these variables are positively related to state

failure- a result that was previously confirmed by other researchers (e.g.,

Howard, 2008). In essence, these colorful maps reveal the existence of

previously theorized assumptions and it can even create new ones. The maps

also make it possible to find subgroups that do not follow the main theoretical

assumptions. For example, when red dots are found in the middle of the

yellow or blue area, this signals the presence of deviant subgroups. When

either blue or red nodes are forming two clearly separated areas, this might be

considered as a sign of non-linear correlation (Thneberg & Hotulainen, 2006).

Figure 15 shows the predictive ability of the SOM model for a randomly

chosen set of the nations included in the analysis. For example, Zimbabwe is

correctly classified as a critically failed nation, while Belgium is correctly

classified as a stable nation (SOM prediction accuracy was 97.74%).

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Table 6. SOM cluster summary

Seg.* Freq

% Dem Ref Gr_Gr Hu_Fl Un_Dev Ec_Dec S_De P_Ser H_Ri Sec_Ap F_El Ex_In

1 21.47 8.18 7.99 8.50 7.17 8.45 7.13 8.69 7.72 8.31 8.18 8.69 7.74

2 37.85 7.51 5.59 6.37 6.30 7.48 6.69 7.53 7.05 6.88 6.65 7.09 6.74

2 20.34 5.94 3.60 4.92 6.14 6.79 5.51 5.83 5.19 4.88 4.65 4.82 5.46

3 20.34 3.45 2.48 3.69 2.53 4.10 3.41 2.94 2.44 2.98 2.21 2.83 3.03

Seg*: 1= critical; 2 = in danger; 3 =borderline; and 4 = stable.

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Mohamed M. Mostafa 76

Figure 14. SOM temperature maps.

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Modeling Nations’ Failure via Data Mining Techniques 77

Figure 15. SOM prediction maps.

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Mohamed M. Mostafa 78

4. IMPLICATIONS, LIMITATIONS AND FUTURE RESEARCH

Our results confirm the theoretical work by Hecht-Nielson (1989) who has

shown that computational intelligence models can learn input-output

relationships to the point of making perfect forecasts with the data on which

the network is trained. However, perfect forecasts with the training data do not

guarantee optimal forecasts with the testing data due to differences in the two

data sets. The good performance of these models in predicting and classifying

failed states can be traced to its inherent non-linearity. This makes such

techniques ideal for dealing with non-linear relations that may exist in the

data. Thus, computational intelligence models are needed to better understand

the inner dynamics of failed states at the global level. Our results are also in

line with the findings of other researchers who have investigated the

performance of neuro-computational models compared to other traditional

statistical techniques, such as regression analysis, discriminant analysis, and

logistic regression analysis. For example, in a study of clinical diagnosis of

cancers, Shan et al., (2002) found a hit ratio of 85% for the neural network

model compared to 80% for the LDA model. In a study of credit-scoring

models used in commercial and consumer lending decisions, Bensic et al.,

(2005) compared the performance of logistic regression, neural networks and

decision trees. The neural network model produced the highest hit rate and the

lowest type I error. Similar findings have been reported in a study examining

the performance of neural networks in predicting bankruptcy (Anandarajan et

al., 2001) and diagnosis of acute appendicitis (Sakai et al., 2007).

Based on variable impact analysis, our findings imply that refugees may

have a “billiard effect” on states failure. For example, the civil war in Liberia

hastened the collapse of Sierra Leone, and the flow of refugees from Sierra

Leone disrupted the unstable Guinean government. The Democratic Republic

of Congo has rapidly collapsed in the aftermath of the Rwandan genocide. Our

analysis also highlights the fact that declining democracy as manifested by a

strong security apparatus is correlated with state failure. From both our SOM

and variable impact analysis it is clear that states ruled by a strong security

apparatus are far more likely to fail than stable democracies. We found that

uneven development has an important impact on states’ failure. This finding is

in line with van de Walle’s (2004) findings. Van de Walle argues that poorly

executed macro-economic policies can lead to the failure of the state until the

state ceases to provide virtually any public goods, and state agents become

entirely predatory through rent seeking and corruption.

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Modeling Nations’ Failure via Data Mining Techniques 79

Despite the significant contributions of this study, it suffers from a number

of limitations. First, this study has used a cross-sectional rather than a

longitudinal approach. This implies that much more emphasis has been placed

on observing failure across nations rather than in observing changes in states

failure rates. There would seem to be hence a need for much more longitudinal

research to focus on observing changes in states failure over time. Second,

despite the satisfactory performance of the computational intelligence models

in this study, future research might improve the performance of the models

used in this study by integrating fuzzy discriminant analysis and genetic

algorithms (GA) with computational intelligence models. Mirmirani and Li

(2004) pointed out that traditional algorithms search for optimal weight

vectors for a neural network with a given architecture, while GA can yield an

efficient exploration of the search space when the modeler has little apriori

knowledge of the structure of problem domains. Finally, future research might

use other computational intelligence and evolutionary computation models’

architectures such as gene expression programming (GEP) to classify and

predict nations’ failure. GEP was first introduced to the genetic programming

(GP) community by Ferreira (2001). Thus, it is the most recent development in

the field of artificial evolutionary systems (Ferreira, 2004). Due to the

unsupervised character of their learning algorithm and the excellent

visualization ability, GEP models have been recently used in myriad fields.

Examples include particle physics data analysis (Teodorescu & Sherwood,

2008), food processing (Kahyaoglu, 2008), real parameter optimization (Xu et

al., 2009), and chaotic maps analysis (Hardy & Steeb, 2002).

APPENDIX 1. R CODE USED TO IMPLEMENT SVM

fsi<-read.table("c:\\FSI.txt", header=T)

library(e1071)

random.df<-sample(fsi)

nobs<-nrow(fsi)

n.test<-nobs %/% 10

test.df<-fsi[1:n.test,]

diagnosis.df <- subset(test.df,select=Class)

test.df<-subset(test.df, select=-Class)

train.df<-fsi[(n.test+1):nobs,]

cost.v<-c(0.01, 0.1, 1, 10, 100, 1000)

error.cv<-c()

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Mohamed M. Mostafa 80

error.ho<-c()

for (i in cost.v)

{m.cv<-svm(Class~.,

data=fsi,

type="C-classification",

kernel="linear",

cost=i,

cross=10

)

e<-100 - summary(m.cv)$tot.accuracy

error.cv<-c(error.cv,e)

m.ho<-svm(Class ~.,

data=train.df,

type="C-classification",

kernel="linear",

cost=i,

cross=0

)

p<-predict(m.ho, test.df)

correct<-sum(p == diagnosis.df[[1]])

e<-(nrow(test.df) - correct)/nrow(test.df)*100

error.ho<-c(error.ho,e)

}

y<-max(error.ho, error.cv)

plot.new()

plot.window(xlim=c(1, length(cost.v)), ylim=c(0,y))

box()

title(xlab="SVM model complexity",ylab="Error rate")

xticks<-seq(1, length(cost.v),1)

yticks<-seq(0,y,1)

xlabels<-seq(1, length(cost.v),1)

ylabels<-seq(0,y,1)

axis(1,at=xticks,labels=xlabels)

axis(2,at=yticks,labels=ylabels)

points(1:length(cost.v),error.cv,type="b",col="red")

points(1:length(cost.v),error.ho,type="b",col="blue")

x<-fsi[, 2:13]

y<-fsi[, 14]

model<-svm(x, y)

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Modeling Nations’ Failure via Data Mining Techniques 81

print(model)

summary(model)

pred<-predict(model, x)

table(pred, y)

tobj<-tune.svm(Class~.,data=fsi[1:100,], gamma=10^(-6:-3),

cost=10^(1:2))

summary(tobj)

plot(tobj, transform.x = log10, xlab=expression(log[10](gamma)),

ylab="C")

APPENDIX 2. R CODE USED TO IMPLEMENT SOM

library(kohonen)

fsi<-read.table("c:\\FSI09.txt", header=T)

kohmap<-xyf(scale(fsi), classvec2classmat(Class), grid = somgrid(6, 6,

"hexagonal"), rlen=100)

plot(kohmap, type="changes" )

plot(kohmap, type="counts", main="Failed states data: counts")

plot(kohmap, type="quality", main="Failed states data: quality")

xyfpredictions<-classmat2classvec(predict(kohmap)$unit.predictions)

bgcols<-c("gray", "pink", "lightgreen")

plot(kohmap, type="mapping", col=Class+1, pchs=Class,

bgcol=bgcols[as.integer(xyfpredictions)], main = "mapping plot")

training<-sample(nrow(fsi), 100)

Xtraining<-scale(fsi[training, ])

Xtest<-scale(fsi[-training, ], center=attr(Xtraining, "scaled:center"),

scale=attr(Xtraining, "scaled:scale"))

som.fsi<-som(Xtraining, grid = somgrid(6, 6, "hexagonal"))

som.prediction<-predict(som.fsi, newdata = Xtest, trainX = Xtraining,

trainY = factor(Class [training]))

table(Class[-training], som.prediction$prediction)

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