使用PCA对手写数据集MNIST进行降维降噪

目录

一、 MNIST训练

二、手写识别数据集PCA降噪

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一、 MNIST训练

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代码示例：

import numpy as np
from sklearn.datasets import fetch_openml

#导入数据
mnist = fetch_openml('mnist_784')

X,y = mnist['data'],mnist['target']

X_train = np.array(X[:60000],dtype=float)  #60000个样本，784个维度
y_train = np.array(X[:60000],dtype=float)
X_test = np.array(X[:60000],dtype=float)
y_test = np.array(X[:60000],dtype=float)

# KNN识别
from sklearn.neighbors import KNeighborsClassifier

knn_clf = KNeighborsClassifier()
knn_clf.fit(X_train,y_train)

# %time knn_clf.score(X_test, y_test)

# PCA降维
from sklearn.decomposition import PCA 

pca = PCA(0.90)
pca.fit(X_train)
X_train_reduction = pca.transform(X_train)
X_test_reduction = pca.transform(X_test)

knn_clf = KNeighborsClassifier()
knn_clf.fit(X_train_reduction, y_train)

%time knn_clf.score(X_test_reduction, y_test)

二、手写识别数据集PCA降噪

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代码示例：

from sklearn import datasets

digites = datasets.load_digits()
X = digits.data
y = digits.target

noisy_digits = X + np.random.normal(0,4,size=X.shape)
example_digits = noisy_digits[y==0,:][:10]

for num in range(1,10):
    X_num = noisy_digits[y==num,:][:10]
    example_digits = np.vstack([example_digits,X_num])

#图形可视化
def plot_digits(data):
    fig, axes = plt.subplots(10,10,figsize=(10,10),subplot_kw = {'xticks':[],'yticks':[]},
    gridspec_kw = dict(hspace=0.1,wspace=0.1))
    for i, ax in enumerate(axes.flat):
        ax.imshow(data[i].reshape(8,8),
                 cmap='binary',interpolation='nearest',clim=(0,16))
    plt.show()
    
plot_digits(example_digits)

运行结果：

代码示例：

#PCA降维

pca = PCA(0.5)
pca.fit(noisy_digits)

components = pca.transform(example_digits)  #降维
filtered_digits = pca.inverse_transform(components)  #低维到高维的恢复，损失的噪音没有了
plot_digits(filtered_digits)

运行结果：