PCA主成分分析
import numpy as npclass PCA:def __init__(self,x,R=None):self.x = np.array(x)self.dim = self.x.shape[-1]self.num = self.x.shape[0]self.R = Rself.X = Noneself.r_list = Noneself.r_v = Noneself.nk = Noneself.X_ = Nonedef standetlize(self):self.X = []for i in range(self.dim):mean = np.mean(self.x[:,i])sii = 1/(self.num-1) * np.sum((self.x[:,i] - mean)**2)self.X.append((self.x[:, i]-mean)/sii)self.X = np.transpose(self.X)def get_R(self):self.R = 1/(self.num-1)*(self.X.T.dot(self.X))def get_r_rv(self,x):x = np.array(x)s_matrix = x.T.dot(x)r_list, r_v = np.linalg.eig(s_matrix)index_rank = np.argsort(-r_list)r_list = r_list[index_rank]r_v = r_v.T[index_rank]return r_list,r_vdef fit(self,k=None,sup=None,way='R'):self.standetlize()if way == 'R':self.get_R()r_list,r_v = self.get_r_rv(self.R)nk = r_list/np.sum(r_list)if sup:for i in range(len(nk)):if np.sum(nk[:i+1]) > sup:k = i+1breakif k:r_v = r_v[:k]r_list = r_list[:k]self.r_v = r_vself.r_list = r_listself.nk = nk[:k]y = []for i in range(k):y.append(r_v[i].dot(self.X.T))y = np.transpose(y)if way == 'SVD':self.X_ = 1/np.sqrt(self.num-1)*self.Xu,s,v = np.linalg.svd(self.X_)y = v[:,:k].T.dot(self.X.T)y = np.transpose(y)return ydef get_rv(self):return self.r_vdef get_r_list(self):return self.r_listdef get_nk(self):return self.nkdef get_factor_loading(self):return [np.sqrt(self.r_list[i])*(self.r_v[i]) for i in range(len(self.r_list))]def get_vi(self):return np.sum([(np.sqrt(self.r_list[i]) * (self.r_v[i]))**2 for i in range(len(self.r_list))],0)def main():x = [[2,9,2],[3,4,5],[3,5,2],[4,5,9],[5,6,1],[7,8,0]]pca = PCA(x)print(pca.fit(sup=0.7))print(pca.get_factor_loading())print(pca.get_vi())print(pca.fit(k=2,way="SVD"))if __name__ == '__main__':main()#----------result----------------/usr/bin/python3 /Users/zhengyanzhao/PycharmProjects/tongjixuexi/shixian2/PVC.py[[ 0.01436405 -0.98056186][-0.62392994 0.24417043][-0.37825673 0.00160078][-0.35639953 0.32072976][ 0.27000345 0.20323966][ 1.0742187 0.21082123]][array([ 0.27913238, 0.22163074, -0.1237391 ]), array([ 0.15944099, -0.1768521 , 0.04290707])][0.10333632 0.08039685 0.01715238][[ 0.01887854 -0.95392328][-0.58760185 0.29494971][-0.44973126 0.00587801][-0.1366 0.41115041][ 0.17525954 0.14729349][ 0.97520268 0.09465167]]
