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| 1 | +#!/usr/bin/env python |
| 2 | +# coding: utf-8 |
| 3 | + |
| 4 | +# ### Principal component analysis (PCA) |
| 5 | +# |
| 6 | +# * PCA is used to decompose a multivariate dataset in a set of successive orthogonal components that explain a maximum amount of the variance. In scikit-learn, PCA is implemented as a transformer object that learns `n` components in its fit method, and can be used on new data to project it on these components. |
| 7 | +# |
| 8 | +# PCA centers but does not scale the input data for each feature before applying the SVD. The optional parameter whiten=True makes it possible to project the data onto the singular space while scaling each component to unit variance. This is often useful if the models down-stream make strong assumptions on the isotropy of the signal: this is for example the case for Support Vector Machines with the RBF kernel and the K-Means clustering algorithm. |
| 9 | +# |
| 10 | +# Below is an example of the iris dataset, which is comprised of 4 features, projected on the 2 dimensions that explain most variance: |
| 11 | + |
| 12 | +# In[2]: |
| 13 | + |
| 14 | + |
| 15 | +get_ipython().system('pip install numpy') |
| 16 | +get_ipython().system('pip install pandas ') |
| 17 | +get_ipython().system('pip install matplotlib ') |
| 18 | +get_ipython().system('pip install scikit-learn') |
| 19 | + |
| 20 | + |
| 21 | +# In[3]: |
| 22 | + |
| 23 | + |
| 24 | +import numpy as np |
| 25 | +import pandas as pd |
| 26 | +import matplotlib.pyplot as plt |
| 27 | + |
| 28 | +from sklearn import datasets |
| 29 | +from sklearn.decomposition import PCA |
| 30 | +from sklearn.discriminant_analysis import LinearDiscriminantAnalysis |
| 31 | + |
| 32 | + |
| 33 | +# In[5]: |
| 34 | + |
| 35 | + |
| 36 | +iris = datasets.load_iris() |
| 37 | + |
| 38 | + |
| 39 | +# In[6]: |
| 40 | + |
| 41 | + |
| 42 | +iris.keys() |
| 43 | + |
| 44 | + |
| 45 | +# In[7]: |
| 46 | + |
| 47 | + |
| 48 | +X = iris.data |
| 49 | +y = iris.target |
| 50 | + |
| 51 | + |
| 52 | +# In[8]: |
| 53 | + |
| 54 | + |
| 55 | +target_names = iris.target_names |
| 56 | + |
| 57 | + |
| 58 | +# In[9]: |
| 59 | + |
| 60 | + |
| 61 | +X.shape # 150 rows and 4 columns |
| 62 | + |
| 63 | + |
| 64 | +# In[10]: |
| 65 | + |
| 66 | + |
| 67 | +pca = PCA(n_components=2) # 150 rows and 2 columns |
| 68 | + |
| 69 | + |
| 70 | +# In[11]: |
| 71 | + |
| 72 | + |
| 73 | +X_r = pca.fit_transform(X) |
| 74 | +X_r.shape |
| 75 | + |
| 76 | + |
| 77 | +# In[23]: |
| 78 | + |
| 79 | + |
| 80 | +lda = LinearDiscriminantAnalysis(n_components=2) |
| 81 | +X_r2 = lda.fit(X,y).transform(X) |
| 82 | + |
| 83 | + |
| 84 | +# In[14]: |
| 85 | + |
| 86 | + |
| 87 | +# Percentage of variance explained for each components |
| 88 | +print('explained variance ratio (first two components): %s' |
| 89 | + % str(pca.explained_variance_ratio_)) |
| 90 | + |
| 91 | + |
| 92 | +# In[24]: |
| 93 | + |
| 94 | + |
| 95 | +plt.figure() |
| 96 | +colors = ['navy', 'turquoise', 'darkorange'] |
| 97 | +lw = 2 |
| 98 | + |
| 99 | +for color, i, target_name in zip(colors, [0, 1, 2], target_names): |
| 100 | + plt.scatter(X_r[y == i, 0], X_r[y == i, 1], color=color, alpha=.8, lw=lw, |
| 101 | + label=target_name) |
| 102 | +plt.legend(loc='best', shadow=False, scatterpoints=1) |
| 103 | +plt.title('PCA of IRIS dataset') |
| 104 | + |
| 105 | +plt.figure() |
| 106 | +for color, i, target_name in zip(colors, [0, 1, 2], target_names): |
| 107 | + plt.scatter(X_r2[y == i, 0], X_r2[y == i, 1], alpha=.8, color=color, |
| 108 | + label=target_name) |
| 109 | +plt.legend(loc='best', shadow=False, scatterpoints=1) |
| 110 | +plt.title('LDA of IRIS dataset') |
| 111 | + |
| 112 | +plt.show() |
| 113 | + |
| 114 | + |
| 115 | +# In[ ]: |
| 116 | + |
| 117 | + |
| 118 | + |
| 119 | + |
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