Question

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).

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

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);

I get the following error:

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

Answer 1

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

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

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