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https://github.com/Visualize-ML/Book4_Power-of-Matrix.git
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185 lines
3.9 KiB
Python
185 lines
3.9 KiB
Python
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch10_01.py
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import seaborn as sns
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import numpy as np
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import matplotlib.pyplot as plt
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import pandas as pd
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from sklearn.datasets import load_iris
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# A copy from Seaborn
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iris = load_iris()
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X = iris.data
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y = iris.target
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feature_names = ['Sepal length, x1','Sepal width, x2',
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'Petal length, x3','Petal width, x4']
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# Convert X array to dataframe
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X_df = pd.DataFrame(X, columns=feature_names)
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#%% Original data, X
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X = X_df.to_numpy();
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# Gram matrix, G and orthogonal basis V
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G = X.T@X
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D, V = np.linalg.eig(G)
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#%%
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def heatmap(Matrices,Titles,Ranges,Equal_tags):
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M1 = Matrices[0]
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M2 = Matrices[1]
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M3 = Matrices[2]
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Title_1 = Titles[0]
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Title_2 = Titles[1]
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Title_3 = Titles[2]
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fig, axs = plt.subplots(1, 5, figsize=(12, 3))
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plt.sca(axs[0])
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ax = sns.heatmap(M1,cmap='RdYlBu_r',
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vmin = Ranges[0][0],
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vmax = Ranges[0][1],
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cbar=False,
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xticklabels=False,
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yticklabels=False)
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if Equal_tags[0] == True:
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ax.set_aspect("equal")
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plt.title(Title_1)
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plt.sca(axs[1])
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plt.title('=')
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plt.axis('off')
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plt.sca(axs[2])
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ax = sns.heatmap(M2,cmap='RdYlBu_r',
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vmin = Ranges[1][0],
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vmax = Ranges[1][1],
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cbar=False,
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xticklabels=False,
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yticklabels=False)
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if Equal_tags[1] == True:
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ax.set_aspect("equal")
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plt.title(Title_2)
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plt.sca(axs[3])
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plt.title('@')
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plt.axis('off')
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plt.sca(axs[4])
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ax = sns.heatmap(M3,cmap='RdYlBu_r',
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vmin = Ranges[2][0],
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vmax = Ranges[2][1],
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cbar=False,
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xticklabels=False,
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yticklabels=False)
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if Equal_tags[2] == True:
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ax.set_aspect("equal")
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plt.title(Title_3)
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#%%
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def plot_four_figs(X,v_j,idx):
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# Fig 1: X@v_j = z_j
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z_j = X@v_j
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Titles = ['$X$',
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'$v_' + str(idx) + '$',
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'$z_' + str(idx) + '$']
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Ranges = [[-2,11],
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[-1,1],
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[-2,11]]
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Equal_tags = [False,True,False]
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heatmap([X,v_j,z_j],Titles,Ranges,Equal_tags)
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# Fig 2: z@v_j.T = X_j
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X_j = z_j@v_j.T
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Titles = ['$z_' + str(idx) + '$',
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'$v_' + str(idx) + '^T$',
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'$X_' + str(idx) + '$']
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Ranges = [[-2,11],
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[-1,1],
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[-2,11]]
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Equal_tags = [False,True,False]
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heatmap([z_j,v_j.T,X_j],Titles,Ranges,Equal_tags)
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# Fig 3: T_j = v_j@v_j.T
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T_j = v_j@v_j.T
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Titles = ['$v_' + str(idx) + '$',
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'$v_' + str(idx) + '^T$',
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'$T_' + str(idx) + '$']
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Ranges = [[-1,1],
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[-1,1],
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[-1,1]]
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Equal_tags = [True,True,True]
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heatmap([v_j,v_j.T,T_j],Titles,Ranges,Equal_tags)
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# Fig 4: X@T_j = X_j
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T_j = X@T_j
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Titles = ['$X$',
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'$T_' + str(idx) + '$',
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'$X_' + str(idx) + '$']
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Ranges = [[-2,11],
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[-1,1],
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[-2,11]]
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Equal_tags = [False,True,False]
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heatmap([X,T_j,X_j],Titles,Ranges,Equal_tags)
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#%% First basis vector
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v1 = V[:, 0].reshape((-1, 1))
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plot_four_figs(X,v1,1)
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#%% Second basis vector
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v2 = V[:, 1].reshape((-1, 1))
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plot_four_figs(X,v2,2)
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#%% Third basis vector
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v3 = V[:, 2].reshape((-1, 1))
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plot_four_figs(X,v3,3)
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#%% Fourth basis vector
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v4 = V[:, 3].reshape((-1, 1))
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plot_four_figs(X,v4,4)
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