I was reading a stats book that mentioned Mahalanobis distance and that made me think of Non Nobis from Henry V, a great scene in a great movie. As far as I know, there’s no connection between Mahalanobis and Non Nobis except that both end in “nobis.”
Since Mahalanobis is an Indian surname and Non Nobis is Latin, there’s probably no etymological connection between the two except maybe way back in Indo-European.
Mahalanobis distance is Euclidean distance adapted to a multivariate normal distribution. Specifically, the squared distance between two column vectors x and y is
(x – y)T S-1 (x – y)
where S is the covariance matrix for a multivariate Gaussian distribution.
You might look at this and ask why the matrix in the middle has to be the inverse of a covariance matrix. Couldn’t it be any invertible matrix? Isn’t this just Euclidean distance in transformed coordinates? Yes and yes. But Mahalanobis thought of how to use it in statistics.
Mahalanobis’ birthday, June 29, is National Statistics Day in India in his honor.
2 thoughts on “Mahalanobis distance and Henry V”
Mahalanobis distance is derived quite intuitively as a generalisation of T statistic for multiple variables.
“Mahalanobis was born on June 29, 1893, into a well-off family in Calcutta (now Kolkata) that reportedly traced the roots of its name to a Mughal-era ancestor who kept land revenue records in ancient Bengal. At the time, he was known as “Nauvice,” a Persian word meaning scribe of the Mahal (the Mughal court). The last name Mahalanobis evolved from the combination of “Nauvice” and “Mahal.”