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Delete Book4_Ch10_Python_Codes directory
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Iris Series: Visualize Math -- From Arithmetic Basics to Machine Learning
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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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@@ -1,131 +0,0 @@
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# -*- coding: utf-8 -*-
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"""
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Created on Tue Sep 27 19:46:17 2022
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@author: Work
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"""
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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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import streamlit as st
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import plotly.express as px
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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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def bmatrix(a):
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"""Returns a LaTeX bmatrix
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:a: numpy array
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:returns: LaTeX bmatrix as a string
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"""
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if len(a.shape) > 2:
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raise ValueError('bmatrix can at most display two dimensions')
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lines = str(a).replace('[', '').replace(']', '').splitlines()
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rv = [r'\begin{bmatrix}']
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rv += [' ' + ' & '.join(l.split()) + r'\\' for l in lines]
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rv += [r'\end{bmatrix}']
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return '\n'.join(rv)
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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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np.set_printoptions(suppress=True)
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D = np.diag(D)
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st.latex(r'G = X^T X = ' + bmatrix(G))
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st.latex(r'G = V \Lambda V^T')
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st.latex(r'G = ' +
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bmatrix(np.round(V,2)) + '@' +
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bmatrix(np.round(D,2)) + '@' +
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bmatrix(np.round(V.T,2)))
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st.write('Mapped data:')
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st.latex('Z = XV')
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#%%
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Z = X@V
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df = pd.DataFrame(Z, columns = ['PC1','PC2','PC3','PC4'])
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mapping_rule = {0: 'setosa', 1: 'versicolor', 2: 'virginica'}
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df.insert(4, "species", y)
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df['species'] = df['species'].map(mapping_rule)
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#%%
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features = df.columns.to_list()[:-1]
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#%% Table of mapped data
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with st.expander('Mapped data'):
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st.write(df)
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#%% Heatmap
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with st.expander('Heatmap'):
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fig_1 = px.imshow(df.iloc[:,0:4],
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color_continuous_scale='RdYlBu_r')
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st.plotly_chart(fig_1)
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#%% 2D scatter plot
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with st.sidebar:
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st.write('2D scatter plot')
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x_feature = st.radio('Horizontal axis',
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features)
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y_feature = st.radio('Vertical axis',
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features)
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with st.expander('2D scatter plot'):
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fig_2 = px.scatter(df, x=x_feature, y=y_feature, color="species")
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st.plotly_chart(fig_2)
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#%% 3D scatter plot
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with st.expander('3D scatter plot'):
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fig_3 = px.scatter_3d(df,
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x='PC1',
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y='PC2',
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z='PC3',
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color='species')
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st.plotly_chart(fig_3)
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#%% Pairwise scatter plot
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with st.expander('Pairwise scatter plot'):
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fig_4 = px.scatter_matrix(df,
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dimensions=["PC1",
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"PC2",
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"PC3",
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"PC4"],
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color="species")
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st.plotly_chart(fig_4)
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