RBF核PCA训练报错：arrays to stack must be passed as a sequence

错误原因 #

报错出现在np.column_stack()调用处：

X_pc = np.column_stack((eigvecs[:, i] for i in range(n_components)))

np.column_stack()要求传入**序列类型（如列表、元组）**的数组集合，但此处使用的是生成器表达式(eigvecs[:, i] for i in range(n_components))，生成器不属于numpy可直接识别的序列参数类型，导致无法正确解析要堆叠的数组。

修复方案 #

将生成器表达式转换为列表（把圆括号改为方括号），让column_stack能正确识别要堆叠的数组序列：

X_pc = np.column_stack([eigvecs[:, i] for i in range(n_components)])

修复后完整代码 #

import numpy as np
from scipy.spatial.distance import pdist, squareform
from scipy.linalg import eigh
from sklearn.datasets import make_moons
import matplotlib.pyplot as plt

def rbf_kernel_pca(X, gamma, n_components):
    """
    RBF kernel PCA implementation.

    Parameters
    ------------
    X: {NumPy ndarray}, shape = [n_samples, n_features]
        
    gamma: float
      Tuning parameter of the RBF kernel
        
    n_components: int
      Number of principal components to return

    Returns
    ------------
     X_pc: {NumPy ndarray}, shape = [n_samples, k_features]
       Projected dataset   

    """
    # Calculate pairwise squared Euclidean distances
    sq_dists = pdist(X, 'sqeuclidean')

    # Convert pairwise distances into a square matrix.
    mat_sq_dists = squareform(sq_dists)

    # Compute the symmetric kernel matrix.
    K = np.exp(-gamma * mat_sq_dists)

    # Center the kernel matrix.
    N = K.shape[0]
    one_n = np.ones((N, N)) / N
    K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)

    # Obtaining eigenpairs from the centered kernel matrix
    eigvals, eigvecs = eigh(K)
    eigvals, eigvecs = eigvals[::-1], eigvecs[:, ::-1]

    # Collect the top k eigenvectors (projected samples)
    # 修复：将生成器表达式改为列表
    X_pc = np.column_stack([eigvecs[:, i] for i in range(n_components)])

    return X_pc

X, y = make_moons(n_samples=100, random_state=123)

X_kpca = rbf_kernel_pca(X, gamma=15, n_components=2)

fig, ax = plt.subplots(nrows=1,ncols=2, figsize=(7,3))
ax[0].scatter(X_kpca[y==0, 0], X_kpca[y==0, 1], 
            color='red', marker='^', alpha=0.5)
ax[0].scatter(X_kpca[y==1, 0], X_kpca[y==1, 1],
            color='blue', marker='o', alpha=0.5)

ax[1].scatter(X_kpca[y==0, 0], np.zeros((50,1))+0.02, 
            color='red', marker='^', alpha=0.5)
ax[1].scatter(X_kpca[y==1, 0], np.zeros((50,1))-0.02,
            color='blue', marker='o', alpha=0.5)

ax[0].set_xlabel('PC1')
ax[0].set_ylabel('PC2')
ax[1].set_ylim([-1, 1])
ax[1].set_yticks([])
ax[1].set_xlabel('PC1')

plt.tight_layout()
plt.show()

验证结果 #

修复后运行代码，将正常生成核PCA投影后的可视化图像，两个类别在主成分空间中实现有效分离。

内容的提问来源于stack exchange，提问作者tan hongkiat