《模式识别与智能计算》基于PCA的模板匹配法
- 2020 年 1 月 16 日
- 筆記
算法流程：
- 选取各类全体样本组成矩阵X,待测样品
- 计算协方差矩阵S
- 根据S的特征值选取适合的矩阵C
- 使用矩阵C降维
- 采用模板匹配开始多类别分类
算法实现
PCA降维算法
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]
模板匹配算法
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]
划分数据集
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
测试代码
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])
算法结果
True
