In [1]:
import pandas as pd
import numpy as np
from io import StringIO
import numpy.linalg as la
import matplotlib.pyplot as plt
from matplotlib import cm as cm
import seaborn as sns
sns.set(font_scale=2)
plt.style.use('seaborn-whitegrid')
%matplotlib inline

from sklearn.decomposition import PCA
from sklearn.preprocessing import scale

Example from: https://analyticsdefined.com/implementing-principal-component-analysis/

In [2]:
sales = pd.io.parsers.read_csv("Wholesale-customers-data.csv")
sales = sales.drop(["Channel", "Region"], axis=1)
sales.head()
Out[2]:
Fresh Milk Grocery Frozen Detergents_Paper Delicassen
0 12669 9656 7561 214 2674 1338
1 7057 9810 9568 1762 3293 1776
2 6353 8808 7684 2405 3516 7844
3 13265 1196 4221 6404 507 1788
4 22615 5410 7198 3915 1777 5185

Get the list of product types

In [3]:
# Get all the headers
header_labels = sales.columns.values.tolist()
header_labels
Out[3]:
['Fresh', 'Milk', 'Grocery', 'Frozen', 'Detergents_Paper', 'Delicassen']
In [4]:
corr_matrix = sales.corr()
# plot correlation matrix
fig = plt.figure()
ax1 = fig.add_subplot(111)
cax = ax1.imshow(corr_matrix, cmap=cm.get_cmap('jet'))
plt.title('Player attributes')
plt.grid('off')
ax1.set_xticks(np.arange(len(header_labels)))
ax1.set_yticks(np.arange(len(header_labels)))
ax1.set_xticklabels(header_labels,fontsize=6,rotation=90)
ax1.set_yticklabels(header_labels,fontsize=6)
fig.colorbar(cax)

/anaconda3/lib/python3.6/site-packages/matplotlib/cbook/__init__.py:424: MatplotlibDeprecationWarning: 
Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.
  warn_deprecated("2.2", "Passing one of 'on', 'true', 'off', 'false' as a "
Out[4]:
<matplotlib.colorbar.Colorbar at 0x1a1d8497b8>

This is when we want to try PCA!

In [5]:
data = pd.DataFrame(scale(sales), columns=['Fresh', 'Milk', 'Grocery', 'Frozen', 'Detergents_Paper', 'Delicassen'])
In [6]:
pca = PCA(n_components=6).fit(data)
pca_samples = pca.transform(data)
In [7]:
def pca_results(data, pca):
    
    # Dimension indexing
    dimensions = ['Dimension {}'.format(i) for i in range(1,len(pca.components_)+1)]
    
    # PCA components
    components = pd.DataFrame(np.round(pca.components_, 4), columns = data.keys()) 
    components.index = dimensions

    # PCA explained variance
    ratios = pca.explained_variance_ratio_.reshape(len(pca.components_), 1) 
    variance_ratios = pd.DataFrame(np.round(ratios, 4), columns = ['Explained Variance']) 
    variance_ratios.index = dimensions

    # Create a bar plot visualization
    fig, ax = plt.subplots(figsize = (14,8))

    # Plot the feature weights as a function of the components
    components.plot(ax = ax, kind = 'bar')
    ax.set_ylabel("Feature Weights") 
    ax.set_xticklabels(dimensions, rotation=0)

    # Display the explained variance ratios# 
    for i, ev in enumerate(pca.explained_variance_ratio_): 
        ax.text(i-0.40, ax.get_ylim()[1] + 0.05, "Explained Variance\n %.4f"%(ev))
        
    ax.legend(bbox_to_anchor=(1.1, 1.05))

    # Return a concatenated DataFrame
    return pd.concat([variance_ratios, components], axis = 1)

pca_results = pca_results(data, pca)
In [8]:
var_exp = pca.explained_variance_ratio_
plt.bar(range(len(var_exp)),var_exp, align='center', label='individual explained variance');
plt.ylabel('Explained variance ratio');
plt.xlabel('Principal components');
In [9]:
pca = PCA(n_components=2).fit(data)
reduced_data = pca.transform(data)
pca_samples = pca.transform(data)
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2'])
In [10]:
def biplot(data, reduced_data, pca):
    
    fig, ax = plt.subplots(figsize = (14,8))
    
    # scatterplot of the reduced data 
    ax.scatter(x=reduced_data.loc[:, 'Dimension 1'], y=reduced_data.loc[:, 'Dimension 2'], facecolors='b', edgecolors='b', s=70, alpha=0.5)
    
    feature_vectors = pca.components_.T

    # using scaling factors to make the arrows
    arrow_size, text_pos = 7.0, 8.0,

    # projections of the original features
    for i, v in enumerate(feature_vectors):
        ax.arrow(0, 0, arrow_size*v[0], arrow_size*v[1], head_width=0.2, head_length=0.2, linewidth=2, color='red')
        ax.text(v[0]*text_pos, v[1]*text_pos, data.columns[i], color='black', ha='center', va='center', fontsize=18)

    ax.set_xlabel("Dimension 1", fontsize=14)
    ax.set_ylabel("Dimension 2", fontsize=14)
    ax.set_title("PC plane with original feature projections.", fontsize=16);
    return ax

biplot(data, reduced_data, pca)
Out[10]:
<matplotlib.axes._subplots.AxesSubplot at 0x1a218f0518>
In [11]:
def plot_arrow(vector,scale,text_label):
    plt.arrow(0, 0, scale*vector[0], scale*vector[1], head_width=0.5, head_length=0.5, fc='k', ec='k', lw=1)
    plt.text(vector[0]*1.3*scale, vector[1]*1.3*scale, text_label , color='black', ha='center', va='center', fontsize=18)