《模式识别与智能计算》基于PCA的模板匹配法

def pca(x,k=0,percent = 0.9):
    """
    :function: 主成分分析法
    :param X: 数据X  m*n维  n表示特征个数，m表示数据个数
    :param K: K表是要保留的维度
    :param percent： 样本所占比例
    :return: 返回特征向量
    """
    m,n = x.shape
    mean = np.mean(x,axis=0)
    mean.shape = (1,n)
    x_norm = x - mean
    x_norm = x_norm.T  # 将它变成 行列分别为特征的矩阵 便于计算！！！
    cov = np.dot(x_norm, x_norm.T)
    eigval, eigvec = np.linalg.eig(cov)
    index = np.argsort(-eigval)
    eigvec_sort = eigvec[index]
    eigval_sort = eigval[index]
    eigval_ratio = eigval_sort/np.sum(eigval_sort)
    sum = 0
    for i in range(eigval_ratio.shape[0]):
        sum += eigval_ratio[i]
        if sum > percent:
            return eigvec_sort[:,:i+1]

def neartemplet(x_train,y_train,sample):
    """
    :function: 模板匹配法
    :param X_train: 训练集 M*N  M为样本个数 N为特征个数
    :param y_train: 训练集标签 1*M
    :param sample: 待识别样品
    :return: 返回判断类别
    """
    n_train = x_train.shape[0]
    dis = []
    for i in range(n_train):
        dis.append(np.sum((sample-x_train[i,:])**2))
    minIndx = np.argmin(dis)
    return y_train[minIndx]

def train_test_split(x,y,ratio = 3):
    """
    :function: 对数据集划分为训练集、测试集
    :param x: m*n维 m表示数据个数 n表示特征个数
    :param y: 标签
    :param ratio: 产生比例 train:test = 3:1(默认比例)
    :return: x_train y_train  x_test y_test
    """
    n_samples , n_train = x.shape[0] , int(x.shape[0]*(ratio)/(1+ratio))
    train_id = random.sample(range(0,n_samples),n_train)
    x_train = x[train_id,:]
    y_train = y[train_id]
    x_test = np.delete(x,train_id,axis = 0)
    y_test = np.delete(y,train_id,axis = 0)
    return x_train,y_train,x_test,y_test

from sklearn import datasets
from Include.chapter3 import function
import numpy as np

#读取数据
digits = datasets.load_digits()
x , y = digits.data,digits.target

#划分数据集
x_train, y_train, x_test, y_test = function.train_test_split(x,y)
testId = np.random.randint(0, x_test.shape[0])
sample = x_test[testId, :]

eigVec = function.pca(x_train)
mean = np.mean(x,axis=0).reshape((1,64))
#去均值
x_train = x_train - mean
sample = sample - mean
#降维
x_train = np.dot(x_train,eigVec)
sample =  np.dot(sample,eigVec)
#模板匹配
ans = function.neartemplet(x_train,y_train,sample)
print(ans==y_test[testId])

True