PYTHON PROGAMMING

# K-means Cluster Analysis (Python)

from __future__ import division, print_function

# import packages for this example

import pandas as pd # DataFrame operations

from collections import OrderedDict # to create DataFrame with ordered columns

# special plotting methods

from pandas.tools.plotting import scatter_matrix

import numpy as np # arrays and math functions

import matplotlib.pyplot as plt # static plotting

from sklearn import preprocessing

from sklearn.cluster import KMeans

from sklearn import metrics # for silhouette coefficient

# previously obtained data from public-domain source at Stanford University

# 240 student participants' self-ratings on 32 personality attributes

# a review of these data suggests that student survey participants were

# given an adjective check-list with instructions to self-rate such as:

# "Rate the extent to which each adjective describes you. Use a

# 1-to-9 scale, where 1 means 'very much unlike me' and

# 9 means 'very much like me.' "

# source: http://www.stanford.edu/class/psych253/data/personality0.txt

# create Pandas DataFrame from the student data

# define a pandas DataFrame

student_data=pd.read_csv('C:/Users/Jahee Koo/Desktop/MSPA/2018_Winter_410_regression/HW04_Cluster/student_data.csv')

# for fun, add your own data to the student_data

# data frame by self-rating the 32 adjectives on a 1-to-9 scale ...

# this would provide 241 observations

# for example...

# my_data_dict = {"distant":1, "talkative":5, "careless":1, "hardworking":8,

# "anxious":2, "agreeable":6, "tense":1, "kind":7, "opposing":3, "relaxed":5,

# "disorganized":4, "outgoing":5, "approving":3, "shy":1, "disciplined":5,

# "harsh":1, "persevering":9, "friendly":7, "worrying":3, "responsive":6,

# "contrary":2, "sociable":6, "lazy":1, "cooperative":8, "quiet":3,

# "organized":6, "critical":5, "lax":2, "laidback":5, "withdrawn":1,

# "givingup":1, "easygoing":6}

# my_data_frame = pd.DataFrame(my_data_dict, index = [0])

# student_data = pd.concat([student_data, my_data_frame])

print('')

print('----- Summary of Input Data -----')

print('')

# show the object is a DataFrame

print('Object type: ', type(student_data))

# show number of observations in the DataFrame

print('Number of observations: ', len(student_data))

# show variable names

variable = student_data.columns

print('Variable names: ', variable)

# show descriptive statistics

pd.set_option('display.max_columns', None) # do not limit output

print(student_data.describe())

# show a portion of the beginning of the DataFrame

print(student_data.head())

print('')

print('----- K-means Cluster Analysis of Variables -----')

print('')

# it is good practice to standardize variables prior to clustering

# work with standard scores for all cluster variables

# standard scores have zero mean and unit standard deviation

# here we standardize each student's data

standardized_student_data_matrix = preprocessing.scale(student_data)

# transpose of matrix needed for clusters of variables

variable_cluster_data = student_data.T

# specify the number of clusters in order to perform

# K-means cluster analysis on the variables in the study

# there is much psychological research about what are called

# the big five factors of perosnality:

# extraversion, agreeableness, conscientiousness, neuroticism, openness

#

# some personality researchers have focused on only two factors:

# extraversion/introversion and neuroticism

# suppose we think five factors (and five clusters) will be sufficient

# here we use our knowledge of the big-five personality factors

# assuming that there may well be five clusters to identify

kmeans = KMeans(n_clusters = 5, n_init = 25, random_state = 1)

kmeans.fit(variable_cluster_data)

cluster = kmeans.predict(variable_cluster_data) # cluster ids for variables

# create pandas DataFrame for summarizing the cluster analysis results

#variable_kmeans_solution = pd.DataFrame(OrderedDict([('cluster', cluster),('variable', variable )]))

variable_kmeans_solution = pd.DataFrame(OrderedDict([('cluster', cluster),('variable', variable ) ]))

print(variable_kmeans_solution)

# print results of variable clustering one cluster at a time

for cluster_id in sorted(variable_kmeans_solution.cluster.unique()):

print()

print(variable_kmeans_solution.loc[variable_kmeans_solution['cluster'] == \

cluster_id])

# The silhouette coefficient is a useful general-purpose index

# for evaluating the strength of a clustering solution. The original

# reference is

# Peter J. Rousseeuw (1987). “Silhouettes: a Graphical Aid to the

# Interpretation and Validation of Cluster Analysis”.

# Computational and Applied Mathematics 20: 53–65.

# doi:10.1016/0377-0427(87)90125-7.

# larger positive values of the silhouette coefficient are preferred

# these indicate dense, well separated clusters

# evaluate the clustering solution using the silhouette coefficient

print('Silhouette coefficient for the five-cluster k-means solution: ',

metrics.silhouette_score(variable_cluster_data, cluster,

metric = 'euclidean'))

# a low silhouette coefficient suggests that we may want to try

# kmeans with alternative values for the number of clusters

# or perhaps this problem is not particularly well suited for cluster analysis

print('')

print('----- Selected K-means Cluster Analysis for Student Segments -----')

print('')

# here we are working in much the way we would in a market research

# study looking for market segments... here segments/clusters of students

# it is good practice to standardize variables prior to clustering

# work with standard scores for all cluster variables across students

# standard scores have zero mean and unit standard deviation for all variables

# these were computed earlier in working on the variable clustering

student_cluster_data = student_data

# specify the number of clusters in order to perform

# K-means cluster analysis on the variables in the study

# with no preconceived notions about the number of student segments/clusters

# we search across various cluster analysis solutions defined

# each individual k-means solution is defined by the argument n_clusters

# consider selecting a solution based on the silhouette coefficient

# for more info on silhouette see

# http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html

for nclusters in range(2,21): # search between 2 and 20 clusters/segments

kmeans = KMeans(n_clusters = nclusters, n_init = 25, random_state = 1)

kmeans.fit(student_cluster_data)

segment = kmeans.predict(student_cluster_data) # cluster ids for variables

print('nclusters: ', nclusters, ' silhouette coefficient: ',

metrics.silhouette_score(student_cluster_data, segment,

metric='euclidean'))

# results suggest that a two-cluster/segment solution is best

print('')

print('----- Solution for Two Student Segments -----')

print('')

kmeans = KMeans(n_clusters = 2, n_init = 25, random_state = 1)

kmeans.fit(student_cluster_data)

segment = kmeans.predict(student_cluster_data) # cluster index

# create pandas DataFrame for summarizing the cluster analysis results

# using OrderedDict to preserve the order of column names

student_kmeans_solution = pd.DataFrame(OrderedDict(

[('student', range(0,len(student_cluster_data))),

('segment', segment)]))

print(student_kmeans_solution)

# to interpret the results of the segmentation

# we can review the original ratings data for the two clusters/segments

# merge/join the segment information with the original student data

student_segmentation_data = student_kmeans_solution.join(student_data)

# try printing the means for attributes within each segment

for segment_id in sorted(student_segmentation_data.segment.unique()):

print()

print('Attribute means for segment: ', segment_id)

this_student_segment_data = student_segmentation_data[ \

student_segmentation_data.segment == segment_id]

attributes = this_student_segment_data.ix[:,'distant':'easygoing'].mean()

print(attributes)

centers = kmeans.cluster_centers_

plt.scatter(centers[:,0],centers[:,1], c='black',s=200,alpha=0.5)

#make blobs

#a different example where the data is generated

from sklearn.datasets.samples_generator import make_blobs

X,y_true = make_blobs(n_samples=300,centers=4,cluster_std=.60,random_state=0)

plt.scatter(X[:, 0],X[:, 1], s=50);

print(X)

kmeans.fit(X)

y_kmeans = kmeans.predict(X)

plt.scatter(X[:,0],X[:,1], c = y_kmeans, s=50, cmap = 'viridis')

centers = kmeans.cluster_centers_

plt.scatter(centers[:,0],centers[:,1], c='black',s=200,alpha=0.5);