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MDS.py
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MDS.py
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import numpy as np
import matplotlib.pyplot as plt
# 不知道如何验证正确性，sklearn中的实现方式和西瓜书中不一致,sklearn中用的smacof方法
# 和自己实现的KernelPCA线性核时结果一致
class MDS:
def __init__(self,d_=2):
self.d_=d_
self.Z=None
self.values_=None
self.vectors_=None
# p229 图10.3 MDS算法
def fit(self,X):
m=X.shape[0]
B=X.dot(X.T)
Dist_2=np.zeros((m,m),dtype=np.float32)
for i in range(m):
for j in range(m):
Dist_2[i,j]=B[i,i]+B[j,j]-2*B[i,j]
Dist_i2=np.mean(Dist_2,axis=1).reshape(-1,1)
Dist_j2=np.mean(Dist_2,axis=0).reshape(1,-1)
dist_2=np.mean(Dist_2)
B_new=-0.5*(Dist_2-Dist_i2-Dist_j2+dist_2)
"""
B_new=np.zeros((m,m))
for i in range(m):
for j in range(m):
B_new[i,j]=-0.5*(Dist_2[i,j]-Dist_i2[i,0]-Dist_j2[0,j]+dist_2)
"""
# 用eig和eigh函数分解出的结果符号位不同
values,vectors=np.linalg.eig(B_new)
#values,vectors=np.linalg.eigh(B_new)
idx=np.argsort(values)[::-1]
self.values_=values[idx][:self.d_]
# print('values:',self.values_)
self.vectors_=vectors[:,idx][:,:self.d_]
self.Z=self.vectors_.dot(np.diag(np.sqrt(self.values_))).real
def fit_transform(self,X):
self.fit(X)
return self.Z
if __name__=='__main__':
X=np.array([[0.697,0.460],[0.774,0.376],[0.634,0.264],[0.608,0.318],[0.556,0.215],
[0.403,0.237],[0.481,0.149],[0.437,0.211],[0.666,0.091],[0.243,0.267],
[0.245,0.057],[0.343,0.099],[0.639,0.161],[0.657,0.198],[0.360,0.370],
[0.593,0.042],[0.719,0.103],[0.359,0.188],[0.339,0.241],[0.282,0.257],
[0.748,0.232],[0.714,0.346],[0.483,0.312],[0.478,0.437],[0.525,0.369],
[0.751,0.489],[0.532,0.472],[0.473,0.376],[0.725,0.445],[0.446,0.459]])
X=np.c_[X,X]
mds=MDS(d_=2)
Z=mds.fit_transform(np.array(X))
print(Z)
"""
import sklearn.manifold as manifold
sklearn_MDS=manifold.MDS(n_components=2,metric=True,random_state=False)
Z2=sklearn_MDS.fit_transform(X)
print(Z2)
print('diff:',np.sum((Z-Z2)**2))
"""