我已经编写了Isomap函数,从计算欧氏距离矩阵开始(使用scipy.spatial.distance.cdist),接下来基于K-最近邻方法和Dijkstra算法(确定最短路径),我已经计算了所有路径上的完整距离矩阵,最后我已经完成了Map计算,随后进行了维度缩减。但是,我想使用epsilon代替K-最近邻,如下所示:
Y =异构图(X,ε,d)
· X是一个n × m矩阵,对应于具有m个属性的n个点。
· epsilon是距离矩阵的匿名函数,用于查找邻域的参数(邻域图必须通过消除完整距离图中宽度大于epsilon的边来形成)。
· d是表示输出维数的参数。
· Y是一个n × d矩阵,表示由等距Map产生的嵌入。
先谢谢你
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial.distance import cdist
def distance_Matrix(X):
return cdist(X,X,'euclidean')
def Dijkstra(h):
q = h.copy()
for i in range(ndata):
for j in range(ndata):
k = np.argmin(q[i,:])
while not(np.isinf(q[i,k])):
q[i,k] = np.inf
for l in neighbours[k,:]:
possible = h[i,l] + h[l,k]
if possible < h[i,k]:
h[i,k] = possible
k = np.argmin(q[i,:])
return h
def MDS(D,newdim=2):
n = D.shape[0]
# Torgerson formula
I = np.eye(n)
J = np.ones(D.shape)
J = I-(1/n)*J
B = (-1/2)*np.dot(np.dot(J,D),np.dot(D,J)) # B = -(1/2).JD²J
#
eigenval, eigenvec = np.linalg.eig(B)
indices = np.argsort(eigenval)[::-1]
eigenval = eigenval[indices]
eigenvec = eigenvec[:, indices]
# dimension reduction
K = eigenvec[:, :newdim]
L = np.diag(eigenval[:newdim])
# result
Y = K @ L **(1/2)
return np.real(Y)
def isomap(data,newdim=2,K=12):
ndata = np.shape(data)[0]
ndim = np.shape(data)[1]
d = distance_Matrix(X)
# replace begin
# K-nearest neighbours
indices = d.argsort()
#notneighbours = indices[:,K+1:]
neighbours = indices[:,:K+1]
# replace end
h = np.ones((ndata,ndata),dtype=float)*np.inf
for i in range(ndata):
h[i,neighbours[i,:]] = d[i,neighbours[i,:]]
h = Dijkstra(h)
return MDS(h,newdim)
2条答案
按热度按时间deikduxw1#
尝试将距离矩阵设置为
sklearn.neighbors.radius_neighbors_graph
zf9nrax12#
你好有一个代码与epsilon方法?你能分享吗?谢谢