改进UMAP计算性能
UMAP是一种常用的降维算法,但是对于大规模数据的情况下计算速度很慢。为了改进UMAP的计算性能,可以采用以下策略:
1.使用流行度更高的库:使用Cython、numba等高效的编译代码库来替代python实现的函数,从而提高计算速度。
2.减少计算距离矩阵的次数:距离矩阵的计算是UMAP的核心,因此可以通过降低距离矩阵的维度和使用局部近邻法等方式来减少计算距离矩阵的次数。
3.对数据进行局部采样:对大规模的数据进行采样,然后在采样数据上训练UMAP模型,最后将模型应用到全数据上,从而降低计算时间。
以下是使用Cython编译UMAP算法函数的示例代码:
import numpy as np
from numba import jit, njit
@njit
def Hbeta(D=np.array([]), beta=1.0):
P = np.exp(-D * beta)
sumP = np.sum(P)
H = np.log(sumP) + beta * np.sum(D * P) / sumP
P = P / sumP
return H, P
@njit
def x2p(X=np.array([]), tol=1e-5, perplexity=30.0):
n = X.shape[0]
d = X.shape[1]
sum_X = np.sum(np.square(X), axis=1)
D = np.add(np.add(-2 * np.dot(X, X.T), sum_X).T, sum_X)
P = np.zeros((n, n))
beta = np.ones((n, 1))
logU = np.log(perplexity)
for i in range(n):
betamin = -np.inf
betamax = np.inf
Di = D[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))]
(H, thisP) = Hbeta(Di, beta[i])
Hdiff = H - logU
tries = 0
while np.abs(Hdiff) > tol and tries < 50:
if Hdiff > 0:
betamin = beta[i]
if betamax == np.inf or betamax == -np.inf:
beta[i] *= 2.0
else:
beta[i] = (beta[i] + betamax) / 2.0
else:
betamax = beta[i]
if betamin == np.inf or betamin == -np.inf:
beta[i] /= 2.0
else:
beta[i] = (beta[i] + betamin) / 2.0
(H, thisP) = Hbeta(Di, beta[i])
Hdiff = H - logU
tries += 1
P[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))] = thisP
return P
@jit
def UMAP(X=np.array([]), n_neighbors=15, min_dist=0.1, metric='euclidean', random_state=None):
from sklearn.utils import check_random