如何在没有一个分量的情况下反演主成分分析？

Question

我想通过应用PCA对信号进行去噪，然后删除一个分量，然后将PCA反向，得到去噪后的信号。 以下是我尝试过的：

reduced = pca.fit_transform(signals)
denoised = np.delete(reduced, 0, 1)
result = pca.inverse_transform(denoised)

但我有一个错误：

ValueError: shapes (11,4) and (5,5756928) not aligned: 4 (dim 1) != 5 (dim 0)

如何反转PCA

Answer 1

要去除噪声，首先为许多组件（pca = PCA(n_components=2)）拟合PCA。然后，查看特征值并识别噪声分量

在识别出这些嘈杂的组件后（写下它），转换整个数据集

例如：

import numpy as np
from sklearn.decomposition import PCA


X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
pca = PCA(n_components=2)
pca.fit(X)

eigenvalues = pca.explained_variance_
print(eigenvalues)
#[7.93954312 0.06045688] # I assume that the 2nd component is noise due to λ=0.06 << 7.93

X_reduced = pca.transform(X)

#Since the 2nd component is considered noise, keep only the projections on the first component
X_reduced_selected = X_reduced[:,0]

要反转，请使用以下命令：

pca.inverse_transform(X_reduced)[:,0]