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MFA.py
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MFA.py
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#coding=utf-8
import numpy as np
from scipy.spatial.distance import euclidean
from scipy.linalg import svd
def initial_W(n):
return np.zeros([n,n]), np.zeros([n,n])
def compute_W(W_1,W_2,la,lb,D,k1,k2):
for i in range(len(D)):
k_1 , k_2, indexNow = 0,0,i
for j in range(len(D[i])):
if j == i:continue
if k_1 < k1 and k_2 < k2:
if D[i,j] in la:
W_1[i,D[i,j]] = 1
k_1 += 1
elif D[i,j] in lb:
W_2[i,D[i,j]] = 1
k_2 += 1
elif k_1 < k1:
W_1[i,D[i,j]] = 1
k_1 += 1
elif k_2 < k2:
W_2[i,D[i,j]] = 1
k_2 += 1
else:
break
return W_1,W_2
def construct(data,n):
D = np.zeros([n,n])
#计算每个点和其他点的距离
for row in range(len(data)):
for col in range(len(data)):
D[row,col] = euclidean(data[row],data[col])
#排序D
D = np.argsort(D,axis=1)
return D
def contructlabelList(label):
u = np.unique(label)
l = []
for i in u:
l.append(np.argwhere(label==i))
return l[0],l[1]
def compute_D(W_1,W_2):
d_1 = np.sum(W_1,axis=1)
d_2 = np.sum(W_2,axis=1)
return np.diag(d_1),np.diag(d_2)
def MFA(data,label,k1,k2,geshu):
'''
:param data: 数据 样本*特征 (n*m)
:param k1: 类内
:param k2: 类间
:return: 投影矩阵
'''
n,m = np.shape(data)[0],np.shape(data)[1]
#构造一个距离矩阵 D --> n*n
D = construct(data,n)
#构建类标存储list 即每个类的所有样本点的类标存储在一个list中
la,lb = contructlabelList(label)
#首先初始化两个矩阵 W_1,W_2, W_1放类内的距离相关值,W_2放类间距离相关值, 维度(n*n)
W_1,W_2 = initial_W(n)
#计算和每个样本点同类的最小距离k1个样本点,结果放入W_1, 不同类的最小距离k2个样本点, 结果放入W_2
W_1,W_2 = compute_W(W_1,W_2,la.flatten(),lb.flatten(),D,k1,k2)
#计算D_1,D_2
D1,D2 = compute_D(W_1,W_2)
intra = reduce(lambda a,b:np.dot(a,b),[data.T,D1-W_1,data])
inter = reduce(lambda a,b:np.dot(a,b),[data.T,D2-W_2,data])
a = np.dot(np.linalg.pinv(inter),intra)
_,_,v = svd(a)
return v[:,:geshu]