From 7a1325151003e13ba52c0dd825c9aa237f3a3cc4 Mon Sep 17 00:00:00 2001 From: Visualize-ML <105787223+Visualize-ML@users.noreply.github.com> Date: Mon, 18 Jul 2022 09:49:53 -0400 Subject: [PATCH] Add files via upload --- Book4_Ch10_Python_Codes/Bk4_Ch10_01.py | 184 ++++++++++++++++++ ...据投影__数学要素__从加减乘除到机器学习.pdf | Bin 0 -> 953506 bytes 2 files changed, 184 insertions(+) create mode 100644 Book4_Ch10_Python_Codes/Bk4_Ch10_01.py create mode 100644 Book4_Ch10_数据投影__数学要素__从加减乘除到机器学习.pdf diff --git a/Book4_Ch10_Python_Codes/Bk4_Ch10_01.py b/Book4_Ch10_Python_Codes/Bk4_Ch10_01.py new file mode 100644 index 0000000..237f363 --- /dev/null +++ b/Book4_Ch10_Python_Codes/Bk4_Ch10_01.py @@ -0,0 +1,184 @@ + +############### +# Authored by Weisheng Jiang +# Book 4 | From Basic Arithmetic to Machine Learning +# Published and copyrighted by Tsinghua University Press +# Beijing, China, 2022 +############### + +# Bk4_Ch10_01.py + +import seaborn as sns +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +from sklearn.datasets import load_iris + +# A copy from Seaborn +iris = load_iris() + +X = iris.data +y = iris.target + +feature_names = ['Sepal length, x1','Sepal width, x2', + 'Petal length, x3','Petal width, x4'] + +# Convert X array to dataframe +X_df = pd.DataFrame(X, columns=feature_names) + +#%% Original data, X + +X = X_df.to_numpy(); + +# Gram matrix, G and orthogonal basis V + +G = X.T@X +D, V = np.linalg.eig(G) + +#%% + +def heatmap(Matrices,Titles,Ranges,Equal_tags): + + M1 = Matrices[0] + M2 = Matrices[1] + M3 = Matrices[2] + + Title_1 = Titles[0] + Title_2 = Titles[1] + Title_3 = Titles[2] + + fig, axs = plt.subplots(1, 5, figsize=(12, 3)) + + plt.sca(axs[0]) + ax = sns.heatmap(M1,cmap='RdYlBu_r', + vmin = Ranges[0][0], + vmax = Ranges[0][1], + cbar=False, + xticklabels=False, + yticklabels=False) + + if Equal_tags[0] == True: + ax.set_aspect("equal") + + plt.title(Title_1) + + plt.sca(axs[1]) + plt.title('=') + plt.axis('off') + + plt.sca(axs[2]) + ax = sns.heatmap(V,cmap='RdYlBu_r', + vmin = Ranges[1][0], + vmax = Ranges[1][1], + cbar=False, + xticklabels=False, + yticklabels=False) + if Equal_tags[1] == True: + ax.set_aspect("equal") + plt.title(Title_2) + + plt.sca(axs[3]) + plt.title('@') + plt.axis('off') + + plt.sca(axs[4]) + ax = sns.heatmap(V.T,cmap='RdYlBu_r', + vmin = Ranges[2][0], + vmax = Ranges[2][1], + cbar=False, + xticklabels=False, + yticklabels=False) + + if Equal_tags[2] == True: + ax.set_aspect("equal") + plt.title(Title_3) + +#%% + +def plot_four_figs(X,v_j,idx): + + # Fig 1: X@v_j = z_j + + z_j = X@v_j + Titles = ['$X$', + '$v_' + str(idx) + '$', + '$z_' + str(idx) + '$'] + + Ranges = [[-2,11], + [-1,1], + [-2,11]] + + Equal_tags = [False,True,False] + heatmap([X,v_j,z_j],Titles,Ranges,Equal_tags) + + # Fig 2: z@v_j.T = X_j + X_j = z_j@v_j.T + Titles = ['$z_' + str(idx) + '$', + '$v_' + str(idx) + '^T$', + '$X_' + str(idx) + '$'] + + Ranges = [[-2,11], + [-1,1], + [-2,11]] + + Equal_tags = [False,True,False] + + heatmap([z_j,v_j.T,X_j],Titles,Ranges,Equal_tags) + + # Fig 3: T_j = v_j@v_j.T + T_j = v_j@v_j.T + + Titles = ['$v_' + str(idx) + '$', + '$v_' + str(idx) + '^T$', + '$T_' + str(idx) + '$'] + + Ranges = [[-1,1], + [-1,1], + [-1,1]] + + Equal_tags = [True,True,True] + + heatmap([v_j,v_j.T,T_j],Titles,Ranges,Equal_tags) + + + # Fig 4: X@T_j = X_j + + T_j = X@T_j + + Titles = ['$X$', + '$T_' + str(idx) + '$', + '$X_' + str(idx) + '$'] + + Ranges = [[-2,11], + [-1,1], + [-2,11]] + + Equal_tags = [False,True,False] + + heatmap([X,T_j,X_j],Titles,Ranges,Equal_tags) + + +#%% First basis vector + +v1 = V[:, 0].reshape((-1, 1)) + +plot_four_figs(X,v1,1) + +#%% Second basis vector + +v2 = V[:, 1].reshape((-1, 1)) + +plot_four_figs(X,v2) + +#%% Third basis vector + +v3 = V[:, 2].reshape((-1, 1)) + +plot_four_figs(X,v3) + +#%% Fourth basis vector + +v4 = V[:, 3].reshape((-1, 1)) + +plot_four_figs(X,v4) + diff --git a/Book4_Ch10_数据投影__数学要素__从加减乘除到机器学习.pdf b/Book4_Ch10_数据投影__数学要素__从加减乘除到机器学习.pdf 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