python svm pca实践（一）

好久没写博客了
这里主要用python的sklearn包，来进行简单的svm的分类和pca的降维
svm是常用的分类器，其核心是在分类的时候找到一个最优的超平面，使得所有的样本与超平面之间的距离达到最小。

pca是常用的一种降维的方法，其核心是对去中心化后的数据，求得协方差矩阵，再对协方差矩阵进行特征分解，将最大的几个特征值作为这个样本的的新特征，达到降低数据特征维度的效果

这里用sklearn的digits数据集作为演示数据集

import numpy as np import matplotlib.pyplot as plt from scipy import stats # ***use seaborn plotting style defaults import seaborn as sns; sns.set() from sklearn import decomposition from sklearn.decomposition import PCA from sklearn.datasets import load_digits #********************* KEY IMPORT OF THIS LECTURE******************************** from sklearn import svm # loading handwritten digits dig_data = load_digits() X = dig_data.data # y: the values of the digits, or "ground truth" y = dig_data.target dig_img = dig_data.images print(type(X), X.dtype, X.shape) print(type(dig_img), dig_img.dtype, dig_img.shape) print(type(y), y.dtype, y.shape)

先导入所需要的包，并下载所需要的数据集
这里主要用到digits数据集中的.data,.target,.images属性
.data 为数据集的图像数据，用有1797个数据以一维的形式呈现，每个数据集的长度为64
.target为数据集的标签数据
.image位数据以8x8的形式呈现

dig_data = load_digits() X = dig_data.data y = dig_data.target # This is basically each array in X # getting reshaped into (8, 8). dig_img = dig_data.images print(type(X), X.dtype, X.shape) print(type(y), y.dtype, y.shape) select_idx = 2 # select_idx = 5 # ********************************Separating training data from testing data**************** Xtrain = np.delete(X, select_idx, axis = 0) ytrain = np.delete(y, select_idx) # if you don't do .reshape(1, -1), you get a warning. # B/c the data argument for classifier has to be an array, # even if it's a one-element array. Xtest = X[select_idx].reshape(1, -1) test_img = dig_img[select_idx] ytest = y[select_idx] print('Xtrain.shape, ytrain.shape', Xtrain.shape, ytrain.shape) print('Xtest.shape, ytest.shape', Xtest.shape, ytest.shape) plt.figure(figsize = (4, 4)) plt.imshow(test_img, cmap = 'binary') plt.grid('off') plt.axis('off') # ************************************* The PCA Section ******************************** n_comp = 10 pca = PCA(n_comp) # finding pca axes pca.fit(Xtrain) # projecting training data onto pca axes Xtrain_proj = pca.transform(Xtrain) # projecting test data onto pca axes Xtest_proj = pca.transform(Xtest) print(Xtrain_proj.shape) print(Xtest_proj.shape) # ************************************* The SVM Section ******************************** # instantiating an SVM classifier clf = svm.SVC(gamma=0.001, C=100.) # apply SVM to training data and draw boundaries. clf.fit(Xtrain_proj, ytrain) # Use SVM-determined boundaries to make # a prediction for the test data point. clf.predict(Xtest_proj)

将数据集分成训练集和测试集，将索引为2的数据从整个数据集中剔除作为测试数据集，剩下的数据作为训练数据集，
n_comp为PCA降维后取得维数，
用训练集来训练PCA，再用训练集的模型来对训练集和测试集进行降维，
接着用训练集来训练SVM，并对测试集进行预测

def classify_dig_svm(X, y, dig_img, select_idx, n_comp, plot_test_img = False): dig_data = load_digits() X = dig_data.data y = dig_data.target dig_img = dig_data.images Xtrain = np.delete(X, select_idx, axis = 0) ytrain = np.delete(y, select_idx) Xtest = X[select_idx].reshape(1, -1) test_img = dig_img[select_idx] ytest = y[select_idx] if plot_test_img == True: plt.figure(figsize = (4, 4)) plt.imshow(test_img, cmap = 'binary') plt.grid('off') plt.axis('off') n_comp = 10 pca = PCA(n_comp) pca.fit(Xtrain) Xtrain_proj = pca.transform(Xtrain) # projecting test data onto pca axes Xtest_proj = pca.transform(Xtest) # print(Xtrain_proj.shape) # print(Xtest_proj.shape) # ************************************* The SVM Section ******************************** # instantiating an SVM classifier clf = svm.SVC(gamma=0.001, C=100.) # apply SVM to training data and draw boundaries. clf.fit(Xtrain_proj, ytrain) clf.predict(Xtest_proj) return clf.predict(Xtest_proj) X = dig_data.data y = dig_data.target n_comp = 30 # select_idx = # classify_dig_svm(X, y, dig_img, select_idx, n_comp, plot_test_img = False) counter = 0 tot = 1797 for i in range(tot): if classify_dig_svm(X, y, dig_img, i, n_comp, plot_test_img = False) == y[i]: counter += 1 rate = counter/tot print(rate)

classify_dig_svm的方法是对每个数据进行测试看一下训练出来的pca模型和svm模型的准确性
其实效果还好