python – 如何在这里执行广义特征分解？

我正在尝试实现laplacian eigenmaps算法,该算法包括：

1)构造一个图(我使用kNN并说k个最近邻居有一个边)

2)将每个边缘与重量相关联

3)定义对角线(对角线放置的行的总和)

4)执行广义特征分解(应该是Lv = lambdaDv,其中L和D在下面的代码中计算)

我认为这可以用scipy.linalg.eig(vals)以某种方式解决,但我不明白如何正确输入我的两个矩阵.有人可以帮助我理解如何执行广义特征分解步骤吗？

import numpy as np
import random as r
from math import exp as exp
from scipy.spatial import distance

def rweights((vectors,features)):
    return 1 * np.random.random_sample((vectors,features)) - 0

def vEuclidean(v,m):
   return np.apply_along_axis(lambda x: distance.euclidean(v,x),1,m)

def mEuclideans(m):
   return np.apply_along_axis(lambda v: vEuclidean(v,m),m)

def neighbours(vector,neigh):
   size = (vector.shape[0] - neigh)
   for i in range(1,size):
      vector[np.argmax(vector)] = 0.0
   return vector

def kNN(m,k):
    me = mEuclideans(m)
    return np.array(map(lambda v: neighbours(v,k),me))

def diag(m):
    sums = np.sum(m,1)
    (vectors,features) = m.shape
    zeros = np.zeros(vectors*features).reshape((vectors,features))
    for i in range(features):
        zeros[i][i] = sums[i]
    return zeros

def vectorWeight(v,sigma):
      f = lambda x: exp((-(x)/(sigma**2)))
      size = v.shape[0]
      for i in range(size):
          v[i] = f(v[i])
      return v 

def weight(m):
    return np.array(np.apply_along_axis(lambda v: vectorWeight(v,0.5),m))

if __name__ == "__main__":
    np.random.seed(666)
    m = rweights((5,3))
    w = weight(kNN(m,2))
    D = diag(w)
    L = D-w

解决方法

好,
这个答案得到了沃伦斯的帮助(所以他值得赞扬),但我发现了一个关于光谱聚类的视频 https://www.youtube.com/watch?v=Ln0mgyvXNQE,他在图上使用了laplacian.我认为根据他的结果检查我的实现会很好.因此,我补充说：

from scipy.linalg import eig    

def distanceM():
    return np.array([[0.0,0.8,0.6,0.1,0.0,0.0],[0.8,0.9,[0.6,0.2],[0.1,0.7],[0.0,0.8]
    [0.0,0.2,0.7,0.0]])

if __name__ == "__main__":
    w = distanceM()
    D = diag(w)
    L = D-w
    w,vr = eig(L)
    print vr

我发现我得到了相同的拉普拉斯矩阵,也有相同的特征向量(vr的第二列).