Python中的一维马氏距离 [英] One dimensional Mahalanobis Distance in Python

问题描述

我一直在尝试验证我的代码以计算用 Python 编写的马哈拉诺比斯距离（并仔细检查以比较OpenCV中的结果） ）
我的数据点均为1维（5行x 1列）。

I've been trying to validate my code to calculate Mahalanobis distance written in Python (and double check to compare the result in OpenCV) My data points are of 1 dimension each (5 rows x 1 column).

在 OpenCV（C ++）中，我成功地计算了数据点的维度时的马氏距离。

In OpenCV (C++), I was successful in calculating the Mahalanobis distance when the dimension of a data point was with above dimensions.

下面的代码在矩阵尺寸为5行x 1列的情况下计算马氏距离时未成功。 但是当矩阵中的列数大于1时有效：

The following code was unsuccessful in calculating Mahalanobis distance when dimension of the matrix was 5 rows x 1 column. But it works when the number of columns in the matrix are more than 1:

import numpy;
import scipy.spatial.distance;
s = numpy.array([[20],[123],[113],[103],[123]]);
covar = numpy.cov(s, rowvar=0);
invcovar = numpy.linalg.inv(covar)
print scipy.spatial.distance.mahalanobis(s[0],s[1],invcovar);

我收到以下错误：

Traceback (most recent call last):
  File "/home/abc/Desktop/Return.py", line 6, in <module>
    invcovar = numpy.linalg.inv(covar)
  File "/usr/lib/python2.6/dist-packages/numpy/linalg/linalg.py", line 355, in inv
    return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
IndexError: tuple index out of range

推荐答案

一维马氏距离真的很容易手动计算：

One-dimensional Mahalanobis distance is really easy to calculate manually:

import numpy as np
s = np.array([[20], [123], [113], [103], [123]])
std = s.std()
print np.abs(s[0] - s[1]) / std

（将公式简化为一维情况）。

(reducing the formula to the one-dimensional case).

但是 scipy.spatial.distance 的问题是出于某些原因 np。给定一组1d变量时，cov 返回标量，即零维数组。您要传递2d数组：

But the problem with scipy.spatial.distance is that for some reason np.cov returns a scalar, i.e. a zero-dimensional array, when given a set of 1d variables. You want to pass in a 2d array:

>>> covar = np.cov(s, rowvar=0)

>>> covar.shape
()

>>> invcovar = np.linalg.inv(covar.reshape((1,1)))

>>> invcovar.shape
(1, 1)

>>> mahalanobis(s[0], s[1], invcovar)
2.3674720531046645

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