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Book4_Ch22_Python_Codes/Bk4_Ch22_01.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Thu Jul 21 08:36:10 2022
+
+@author: james
+"""
+
+# Bk4_Ch22_01_A
+
+import numpy as np
+import matplotlib.pyplot as plt 
+import pandas as pd  
+import seaborn as sns 
+from sklearn.datasets import load_iris
+
+# Load the iris data
+iris_sns = sns.load_dataset("iris") 
+# A copy from Seaborn
+iris = load_iris()
+# A copy from Sklearn
+
+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)
+
+#%% Heatmap of X
+
+plt.close('all')
+sns.set_style("ticks")
+
+X = X_df.to_numpy();
+
+# Visualize the heatmap of X
+
+fig, ax = plt.subplots()
+ax = sns.heatmap(X,
+                 cmap='RdYlBu_r',
+                 xticklabels=list(X_df.columns),
+                 cbar_kws={"orientation": "vertical"},
+                 vmin=-1, vmax=9)
+plt.title('X')
+
+#%%
+
+# Bk4_Ch22_01_B
+
+#%% centroid of data matrix, X
+v_1 = np.ones((len(X),1))
+
+E_X = v_1.T@X/len(X)
+# validate: X.mean(axis = 0)
+
+#%% Demean, centralize 
+
+X_demean = X_df.sub(X_df.mean())
+
+
+fig, ax = plt.subplots()
+ax = sns.heatmap(X_demean,
+                 cmap='RdYlBu_r',
+                 xticklabels=list(X_df.columns),
+                 cbar_kws={"orientation": "vertical"},
+                 vmin=-3, vmax=3)
+plt.title('$X_{demean}$')
+
+#%% SSD
+
+SSD = (np.linalg.norm(X - E_X, axis = 1)**2).sum()
+# validate: ((X - E_X)**2).sum()
+# use trace: np.trace((X - E_X).T@(X - E_X))
+
+#%%
+
+# Bk4_Ch22_01_C
+
+# distribution of column features of X
+
+fig, ax = plt.subplots()
+sns.kdeplot(data=X_demean,fill=True, 
+            common_norm=False, 
+            alpha=.3, linewidth=1,
+            palette = "viridis")
+plt.title('Distribution of $X_{demean}$ columns')
+
+#%%
+
+# Bk4_Ch22_01_D
+
+#%% covariance matrix
+
+SIGMA = X_df.cov()
+
+fig, axs = plt.subplots()
+
+h = sns.heatmap(SIGMA,cmap='RdBu_r', linewidths=.05, annot = True)
+h.set_aspect("equal")
+h.set_title('$\Sigma$')
+
+
+#%% correlation matrix
+
+RHO = X_df.corr()
+
+fig, axs = plt.subplots()
+
+h = sns.heatmap(RHO,cmap='RdBu_r', linewidths=.05, annot = True)
+h.set_aspect("equal")
+h.set_title('$\u03A1$')
+
+#%% compare covariance matrices
+
+f,(ax1,ax2,ax3) = plt.subplots(1,3,sharey=True)
+
+g1 = sns.heatmap(X_df[y==0].cov(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax1,square=True,
+                 vmax = 0.4, vmin = 0)
+ax1.set_title('Y = 0, setosa')
+
+g2 = sns.heatmap(X_df[y==1].cov(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax2,square=True,
+                 vmax = 0.4, vmin = 0)
+ax2.set_title('Y = 1, versicolor')
+
+g3 = sns.heatmap(X_df[y==2].cov(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax3,square=True,
+                 vmax = 0.4, vmin = 0)
+ax3.set_title('Y = 2, virginica')
+
+#%% compare correlation matrices
+
+f,(ax1,ax2,ax3) = plt.subplots(1,3,sharey=True)
+
+g1 = sns.heatmap(X_df[y==0].corr(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax1,square=True,
+                 vmax = 1, vmin = 0.15)
+ax1.set_title('Y = 0, setosa')
+
+g2 = sns.heatmap(X_df[y==1].corr(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax2,square=True,
+                 vmax = 1, vmin = 0.15)
+ax2.set_title('Y = 1, versicolor')
+
+g3 = sns.heatmap(X_df[y==2].corr(),cmap="RdYlBu_r",
+                 annot=True,cbar=False,ax=ax3,square=True,
+                 vmax = 1, vmin = 0.15)
+ax3.set_title('Y = 2, virginica')