Question

我正在尝试在python上实现PCA。我在mnist数据集上使用KNN分类器来检查我的实现成功但是成功率太低了％10％。你能检查我的代码并说明我做错了吗？

import numpy as np 
from sklearn.neighbors import KNeighborsClassifier

def PCA(data, ndimension): 
    x , y = data.shape
    mean_vec = np.mean(data, axis=0)
    mean_data = data - mean_vec
    cov_mat = mean_data.T.dot(mean_data) / (x-1)
    eig_vals, eig_vecs = np.linalg.eig(cov_mat)
    eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]
    eig_pairs.sort(key=lambda x: x[0], reverse=True)

    matrix_w = eig_pairs[0][1].reshape(y,1)
    for ar in range(1, ndimension):
    matrix_w = np.hstack((matrix_w, eig_pairs[ar][1].reshape(y,1)))

   FinalData = (mean_data.dot(matrix_w))

   return FinalData

xtrain = PCA(train_images,40)
xtest = PCA(test_images, 40)   

r=0
w=0
num = len(xtest)
for i in range(num):
    t = xtest[i]
    j = getNearestSampleIndex(t, xtrain)

    if (np.all(train_labels[j] == test_labels[i])):
        r+=1
    else:
    w+=1

print ("tested ", num, " digits")
print ("correct: ", r, "wrong: ", w, "error rate: ", float(w)*100/(r+w), "%")
print ("got correctly ", float(r)*100/(r+w), "%")

Answer 1

我知道你为什么用x-1划分cp.cov（）而你使用np.hstack，这里我认为是一个非常简单的PCA版本（测试并比较了女巫scikit）每个数据都是一列矢量形状（N，1）

def myPCA(data, n_comp=3):
   d= data - data.mean(axis = 1).reshape(data.shape[0], 1)
   c = np.cov(d)
   eigvals, eigvect = np.linalg.eigh(c)
   ind = np.argsort(eigvals)
   ind = ind[::-1]
   eigvals = eigvals[ind]
   eigvect = eigvect[:,ind]
   data_projected = (d.T @ eigvect[:,:n_comp]).T
   return eigvals[:n_comp], eigvect[:,:n_comp], data_projected

Python PCA实现成功率低

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