機器學習-初級進階（PCA）

一、主成分分析

1. 原理
   
   
   最終不斷壓縮團圓範圍，坐落於橢圓內的點爲主要影響因素，實現降維操作
   

2. 代碼實現

   數據：

   Alcohol,Malic_Acid,Ash,Ash_Alcanity,Magnesium,Total_Phenols,Flavanoids,Nonflavanoid_Phenols,Proanthocyanins,Color_Intensity,Hue,OD280,Proline,Customer_Segment
   14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065,1
   13.2,1.78,2.14,11.2,100,2.65,2.76,0.26,1.28,4.38,1.05,3.4,1050,1
   13.16,2.36,2.67,18.6,101,2.8,3.24,0.3,2.81,5.68,1.03,3.17,1185,1
   14.37,1.95,2.5,16.8,113,3.85,3.49,0.24,2.18,7.8,0.86,3.45,1480,1
   13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735,1
   ...
   此數據爲酒中不同數量成分的組合最終合成酒的種類，共分爲了1，2，3三種不同種類
   

   實現步驟：

   
   代碼：

   from sklearn.model_selection import train_test_split
   from sklearn.linear_model import LogisticRegression
   from sklearn.preprocessing import StandardScaler
   from sklearn.metrics import confusion_matrix
   from matplotlib.colors import ListedColormap
   from sklearn.decomposition import PCA
   import matplotlib.pyplot as plt
   import pandas as pd
   import numpy as np
   
   dataset = pd.read_csv("Wine.csv")
   X = dataset.iloc[:, 0:-1].values
   y = dataset.iloc[:, -1].values
   
   # 劃分數據集爲訓練集和測試集
   X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
   
   # 特徵縮放
   sc_X = StandardScaler()
   X_train = sc_X.fit_transform(X_train)
   X_test = sc_X.transform(X_test)
   
   # 利用PCA對數據降維
   pca = PCA(n_components=2)  # n_components: 新的自變量的個數
   X_train = pca.fit_transform(X_train)
   X_test = pca.transform(X_test)
   explained_varance = pca.explained_variance_ratio_  # 解釋方差的百分比, 用來確定新自變量的個數
   
   # 邏輯迴歸擬合數據
   classifier = LogisticRegression(random_state=0)
   classifier.fit(X_train, y_train)
   
   # 預測測試集
   y_pred = classifier.predict(X_test)
   
   # 構建混淆矩陣
   cm = confusion_matrix(y_test, y_pred)
   
   # 畫圖
   X_set, y_set = X_train, y_train
   X1, X2 = np.meshgrid(np.arange(start=X_set[:, 0].min() - 1, stop=X_set[:, 0].max() + 1, step=0.01),
                        np.arange(start=X_set[:, 1].min() - 1, stop=X_set[:, 1].max() + 1, step=0.01))
   plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
                alpha=0.75, cmap=ListedColormap(('red', 'green', 'black')))
   plt.xlim(X1.min(), X1.max())
   plt.ylim(X2.min(), X2.max())
   for i, j in enumerate(np.unique(y_set)):
       plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                   c=ListedColormap(('orange', 'blue', 'grey'))(i), label=j)
   plt.title('Logistic Regression (Training set)')
   plt.xlabel('pc1')
   plt.ylabel('pc2')
   plt.legend()
   plt.show()
   
   
   X_set, y_set = X_test, y_test
   X1, X2 = np.meshgrid(np.arange(start=X_set[:, 0].min() - 1, stop=X_set[:, 0].max() + 1, step=0.01),
                        np.arange(start=X_set[:, 1].min() - 1, stop=X_set[:, 1].max() + 1, step=0.01))
   plt.contourf(X1, X2, classifier.predict(np.array([X1.ravel(), X2.ravel()]).T).reshape(X1.shape),
                alpha=0.75, cmap=ListedColormap(('red', 'green', 'black')))
   plt.xlim(X1.min(), X1.max())
   plt.ylim(X2.min(), X2.max())
   for i, j in enumerate(np.unique(y_set)):
       plt.scatter(X_set[y_set == j, 0], X_set[y_set == j, 1],
                   c=ListedColormap(('orange', 'blue', 'grey'))(i), label=j)
   plt.title('Logistic Regression (Test set)')
   plt.xlabel('pc1')
   plt.ylabel('pc2')
   plt.legend()
   plt.show()
   

   輸出結果：
   訓練結果
   
   測試結果：