The file "customerdata.csv" contains 9 columns. The first column is the customer index, next seven columns are the attributes of information about each customer, and the last column tells that whether the customer requires an intervention or not. The information whether the customer requires an intervention or not is provided based on a survey. The company wants to understand if the attributes of the customer can guide them towards understanding whether intervention is required. Such an understanding will help them avoid unnecessary surveys in the future.

The objective is to find out the 7 different principal components and their explained variances. Principal component analysis is commonly used for data compression. It is possible to visualize the 7 dimensional data using the first two principal components in 2 dimensions with minimum loss of information. Plot the data in two dimensions and see if anything can be said about what kind of customers require intervention.

Loading packages

from sklearn import metrics
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import numpy as np
import csv

Importing datafile as a list object

csvfile = open('customerdata.csv')
# creating a csv reader object
readerobject = csv.reader(csvfile, delimiter=',')
lst = list(readerobject)
csvfile.close()
# removing first row from list
lst = lst[1:]
arr = np.array(lst)
data = arr.astype(float)

intervention=data[:,-1]
# removing first and last column from list
data = data[:,1:-1]
print(np.shape(data))

# normalize the data
data_min = data.min(axis=0)
data_max = data.max(axis=0)
data_norm = (data-data_min)/(data_max-data_min)

#for i in range(0,np.size(data,1)):
#    data_norm[:,i] = (data[:,i]-data_min[i])/(data_max[i]-data_min[i])

(1000, 7)

Identifying the 7 principal components

print(np.shape(data_norm))
#print(data)
#print(data_norm)

#Note that PCA does centering of the data
pca = PCA(n_components=7)
pca.fit(data_norm)

(1000, 7)

PCA(copy=True, iterated_power='auto', n_components=7, random_state=None,
  svd_solver='auto', tol=0.0, whiten=False)

Printing the loadings

#Note that the first two components are similar to customer satisfaction and customer value, respectively
print(pca.components_)

[[-0.00328525  0.46597901 -0.86740711 -0.17306732  0.010641    0.00449094
   0.01928677]
 [ 0.47913522  0.03476629  0.04736982 -0.05098777  0.60271426  0.40369948
   0.48799523]
 [ 0.05886257  0.09253122 -0.14604654  0.9819914   0.0473299   0.00367415
  -0.00910255]
 [-0.27764024 -0.07724586 -0.03475359  0.04297846 -0.31695811 -0.23400424
   0.87101871]
 [-0.06694078  0.87558675  0.47199756 -0.00546035 -0.04651038 -0.04022935
   0.04768279]
 [ 0.44305793  0.00355406  0.0052064  -0.03397487  0.22910469 -0.86601517
  -0.00586469]
 [-0.69934851 -0.02147389 -0.00384734  0.0104686   0.69229152 -0.17502684
  -0.02059577]]

Printing the variances explained by each of the principal components

#Pring the eigen values
print(pca.explained_variance_)
print(pca.explained_variance_ratio_)
plt.bar(x=["PC1","PC2","PC3","PC4","PC5","PC6","PC7"],height=pca.explained_variance_ratio_)
plt.show()

[0.17252592 0.10348626 0.07992296 0.05450644 0.02552347 0.01401692
 0.00590595]
[0.37843932 0.22699934 0.17531275 0.11956106 0.05598628 0.03074642
 0.01295483]

Note that T = XW, where T is the new coordinate system, X is the old coordinate system and W is the weight matrix where the column vectors are the eigen vectors of the matrix X'X

weights = pca.components_
weights = weights.transpose()
T = data_norm.dot(weights[:,:2])

print(T)

[[-0.73739712  0.83146526]
 [-0.08237654  0.33704322]
 [-0.9240241   0.45278157]
 ...
 [-0.90648213  0.58205567]
 [-0.9455266   0.69657884]
 [-0.03365671  0.90558889]]

plt.scatter(T[intervention==0,0],T[intervention==0,1])
plt.scatter(T[intervention==1,0],T[intervention==1,1])
plt.xlabel("Customer Satisfaction")
plt.ylabel("Customer Value")
plt.show()