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#cython: wraparound=False, boundscheck=False, cdivision=True, overflowcheck=False | |
#cython: profile=False, nonecheck=False, cdivision_warnings=True | |
import numpy as np | |
cimport numpy as np | |
from libc.math import sqrt, exp | |
from sklearn.utils.extmath import fast_dot | |
from sklearn.metrics.pairwise import pairwise_distances | |
def diffusion_map(X, n_components=2, metric="euclidean"): | |
distance_matrix = pairwise_distances(X, metric=metric) | |
P = calc_markov_matrix(distance_matrix) | |
evals, evecs = np.eigsh(P, n_components + 1, which="LA") | |
evals, evecs = evals[::-1], evecs[:, ::-1] # largest to smallest | |
evals, evecs = evals[1:], evecs[:, 1:] # discard 1st bc it will always be 1 | |
proj = fast_dot(P, evecs[:, 1:]) | |
return proj | |
def calc_markov_matrix(distance_matrix, epsilon=0.2): | |
N = distance_matrix.shape[0] | |
return np.asarray(_calc_markov_matrix(distance_matrix, epsilon, N)) | |
cdef double[:,:] _calc_markov_matrix(double[:,:] distance_matrix, double epsilon, int N): | |
cdef: | |
int i, j | |
double[:] D = np.zeros(N) | |
double[:] Dtilda = np.zeros(N) | |
double[:,:] K = np.zeros((N,N)) | |
double[:,:] Ktilda = np.zeros((N,N)) | |
double[:,:] P = np.zeros((N,N)) | |
with nogil: | |
for i in range(N): | |
for j in range(N): | |
K[i, j] = exp( (-distance_matrix[i, j]**2) / (2*epsilon**2) | |
D[i] += K[i, j] | |
for i in range(N): | |
for j in range(N): | |
Ktilda[i, j] = K[i, j] / sqrt(D[i]**2) | |
Dtilda[i] += Ktilda[i, j] | |
for i in range(N): | |
for j in range(N): | |
P[i, j] = Ktilda[i, j] / Dtilda[i] | |
return P |
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