多维点的几何中位数 [英] Geometric median of multidimensional points

问题描述

我有3D点数组:

a = np.array([[2., 3., 8.], [10., 4., 3.], [58., 3., 4.], [34., 2., 43.]])

如何计算这些点的几何中位数?

推荐答案

我在他们的论文.一切都以numpy进行矢量化处理，因此应该非常快.我没有实现权重-只是未加权的分数.

I implemented Yehuda Vardi and Cun-Hui Zhang's algorithm for the geometric median, described in their paper "The multivariate L1-median and associated data depth". Everything is vectorized in numpy, so should be very fast. I didn't implement weights - only unweighted points.

import numpy as np
from scipy.spatial.distance import cdist, euclidean

def geometric_median(X, eps=1e-5):
    y = np.mean(X, 0)

    while True:
        D = cdist(X, [y])
        nonzeros = (D != 0)[:, 0]

        Dinv = 1 / D[nonzeros]
        Dinvs = np.sum(Dinv)
        W = Dinv / Dinvs
        T = np.sum(W * X[nonzeros], 0)

        num_zeros = len(X) - np.sum(nonzeros)
        if num_zeros == 0:
            y1 = T
        elif num_zeros == len(X):
            return y
        else:
            R = (T - y) * Dinvs
            r = np.linalg.norm(R)
            rinv = 0 if r == 0 else num_zeros/r
            y1 = max(0, 1-rinv)*T + min(1, rinv)*y

        if euclidean(y, y1) < eps:
            return y1

        y = y1

除了默认的SO许可条款外，如果您愿意，我还根据zlib许可发布了上面的代码.

In addition to the default SO license terms, I release the code above under the zlib license, if you so prefer.

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