In [1]:
import numpy as np

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
import pandas as pd

Example from: http://setosa.io/ev/principal-component-analysis/

In [2]:
data = pd.io.parsers.read_csv("UK_foods.csv")
data.head()
Out[2]:
Unnamed: 0 England Wales Scotland N.Ireland
0 Cheese 105 103 103 66
1 Carcass_meat 245 227 242 267
2 Other_meat 685 803 750 586
3 Fish 147 160 122 93
4 Fats_and_oils 193 235 184 209
In [3]:
headers = data['Unnamed: 0'].values.tolist()
print(headers)

new_data = data.drop(['Unnamed: 0'], axis=1)
new_data.head()

regions = new_data.columns.values.tolist()
print(regions)

['Cheese', 'Carcass_meat ', 'Other_meat ', 'Fish', 'Fats_and_oils ', 'Sugars', 'Fresh_potatoes ', 'Fresh_Veg ', 'Other_Veg ', 'Processed_potatoes ', 'Processed_Veg ', 'Fresh_fruit ', 'Cereals ', 'Beverages', 'Soft_drinks ', 'Alcoholic_drinks ', 'Confectionery ']
['England', 'Wales', 'Scotland', 'N.Ireland']
In [4]:
food = pd.DataFrame(new_data.values.T,columns=headers)
food['region'] = regions
food
Out[4]:
Cheese Carcass_meat Other_meat Fish Fats_and_oils Sugars Fresh_potatoes Fresh_Veg Other_Veg Processed_potatoes Processed_Veg Fresh_fruit Cereals Beverages Soft_drinks Alcoholic_drinks Confectionery region
0 105 245 685 147 193 156 720 253 488 198 360 1102 1472 57 1374 375 54 England
1 103 227 803 160 235 175 874 265 570 203 365 1137 1582 73 1256 475 64 Wales
2 103 242 750 122 184 147 566 171 418 220 337 957 1462 53 1572 458 62 Scotland
3 66 267 586 93 209 139 1033 143 355 187 334 674 1494 47 1506 135 41 N.Ireland

This is when we want to try PCA!

In [5]:
#Performing PCA without scaling the data (to match the results from the website)
X = pd.DataFrame(food[headers], columns=headers)
# In general, PCA scales the variables to zero-mean (use line below to scale)
# X = pd.DataFrame(scale(food[headers]), columns=headers)
In [6]:
pca = PCA().fit(X)
pca_samples = pca.transform(X)
In [7]:
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 [8]:
components = pd.DataFrame(pca.components_, columns = headers) 
components
Out[8]:
Cheese Carcass_meat Other_meat Fish Fats_and_oils Sugars Fresh_potatoes Fresh_Veg Other_Veg Processed_potatoes Processed_Veg Fresh_fruit Cereals Beverages Soft_drinks Alcoholic_drinks Confectionery
0 -0.056955 0.047928 -0.258917 -0.084415 -0.005194 -0.037621 0.401402 -0.151850 -0.243594 -0.026886 -0.036488 -0.632641 -0.047703 -0.026188 0.232244 -0.463968 -0.029650
1 0.016013 0.013916 -0.015331 -0.050755 -0.095389 -0.043022 -0.715017 -0.144900 -0.225451 0.042851 -0.045452 -0.177741 -0.212600 -0.030561 0.555124 0.113537 0.005950
2 0.023943 0.063671 -0.553849 0.039065 -0.125223 -0.036057 -0.206682 0.213822 -0.053328 -0.073649 0.052892 0.400129 -0.358849 -0.041359 -0.169426 -0.498583 -0.052322
3 -0.409383 0.729482 0.331001 0.022376 0.034512 0.024943 0.021396 0.001607 0.031153 -0.017380 0.021251 0.227657 0.100043 -0.018382 0.222319 -0.273126 0.001891
In [9]:
plt.figure()
plt.bar(headers,components.values[0])
plt.xticks(rotation=90)
plt.title('influence of original variables(food) upon pc1')
plt.figure()
plt.bar(headers,components.values[1])
plt.xticks(rotation=90)
plt.title('influence of original variables(food) upon pc2')
Out[9]:
Text(0.5,1,'influence of original variables(food) upon pc2')
In [10]:
Xstar = pd.DataFrame(pca_samples,columns=['pc1','pc2','pc3','pc4'])
Xstar['region'] = regions
Xstar
Out[10]:
pc1 pc2 pc3 pc4 region
0 -144.993152 -2.532999 105.768945 -1.699297e-14 England
1 -240.529148 -224.646925 -56.475555 5.541582e-13 Wales
2 -91.869339 286.081786 -44.415495 -6.694069e-13 Scotland
3 477.391639 -58.901862 -4.877895 1.251362e-13 N.Ireland
In [11]:
sns.stripplot(x="pc1",y="region", data=Xstar, jitter=0.05, linewidth=1)
Out[11]:
<matplotlib.axes._subplots.AxesSubplot at 0x1a15330f98>
In [12]:
ax = plt.figure()
ax = sns.lmplot('pc1', 'pc2',Xstar,hue='region', fit_reg=False)
plt.axis('equal')
plt.xlabel('pc1')
plt.ylabel('pc2')
Out[12]:
Text(67.7201,0.5,'pc2')
<matplotlib.figure.Figure at 0x1a15170a90>
In [13]:
def plot_arrow(v,scale,text_pos,text_label):
    plt.arrow(0, 0, scale*v[0], scale*v[1], head_width=0.2, head_length=0.2, linewidth=2, color='red')
    plt.text(v[0]*text_pos, v[1]*text_pos, text_label, color='black', ha='center', va='center', fontsize=18)
In [14]:
ax = plt.figure()
ax = sns.lmplot('pc1', 'pc2',Xstar,hue='region', fit_reg=False)
plt.axis('equal')
plt.xlabel('pc1')
plt.ylabel('pc2')

lab = ['Fresh_potatoes ',
 'Fresh_fruit ',
 'Soft_drinks ',
 'Alcoholic_drinks ']

for i,label in enumerate(lab):
    plot_arrow(components[label],500,500,label)

<matplotlib.figure.Figure at 0x1a1520dac8>