使用PCA时如何决定是使用训练数据还是测试数据？

编程问答 2022-05-18

问题描述

我是 PCA 的新手，在拟合和转置方面有一个关于可视化的问题。我有两个数据，分别是训练和测试。这里有四种方法：

# Method 1)
pca = myPCA(n_components = 5) # Conduct myPCA with 5 principal components.
pca.fit(X_train) # Calculate 5 principal components on the training dataset
X_train_pca = pca.transform(X_train)

# Method 2)
pca = myPCA(n_components = 5) # Conduct myPCA with 5 principal components.
pca.fit(X_test)
X_test_pca = pca.transform(X_test)

# Method 3)
pca = myPCA(n_components = 5) # Conduct myPCA with 5 principal components.
pca.fit(X_train)
X_test_pca = pca.transform(X_train)

# Method 4)
pca = myPCA(n_components = 5) # Conduct myPCA with 5 principal components.
pca.fit(X_train)
X_test_pca = pca.transform(X_test)

以上4种方法中，哪一种是使用PCA进行可视化的正确方法？虽然PCA的教程明确说需要在测试数据上运行，但是，似乎我可以没有为此编写正确的方法。

这是我的代码：

class myPCA():
"""
Principal Component Analysis (A Linear Dimension Reduction Method).
"""

def __init__(self,n_components = 2):
    """
    Conduct myPCA with 2 principal components(the principal and orthogonal modes of variation).
    """
    self.n_c = n_components


def fit(self,X):
    """
    The procedure of computing the covariance matrix.
    """
    cov_mat = np.cov(X.T) # Covariance matrix
    eig_val,eig_vec = np.linalg.eigh(cov_mat) # Eigen-values and orthogonal eigen-vectors in ascending order.
    eig_val = np.flip(eig_val) # Reverse the order,now it is descending.
    eig_vec = np.flip(eig_vec,axis=1) # reverse the order
    self.eig_values = eig_val[:self.n_c] # select the top eigen-vals
    self.principle_components = eig_vec[:,:self.n_c] # select the top eigen-vecs
    self.variance_ratio = self.eig_values/eig_val.sum() # variance explained by each PC

def transform(self,X):
    """
    Compute the score matrix.
    """
    return np.matmul(X-X.mean(axis = 0),self.principle_components) #project the data (centered) on PCs

可视化代码（仍然不确定下面是使用X_train还是X_test）：

import matplotlib.pyplot as plt
import seaborn as sns; sns.set()
figure = plt.figure(dpi=100)
plt.scatter(X_test_pca[:,0],X_test_pca[:,1],c=y_test,s=15,edgecolor='none',alpha=0.5,cmap=plt.cm.get_cmap('tab10',10))
plt.xlabel('component 1')
plt.ylabel('component 2')
plt.colorbar();

解决方法

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dimensionality-reductionnumpypcapythonscikit-learn