How to calculate the distance of Mahalanobis between two time series of equal sizes?

Question

I am collecting data from time series data. I need to calculate the distance or similarity between two rows of equal sizes. I was offered to use the Euclidean distance, similarity or the distance of the Mahalanobi. The first two did not provide any useful information. I don’t seem to understand the various textbooks on the Internet.

So,

For two vectors A (a1, a2, a3, ..., an) and B (b1, b2, b3, ..., bn), how do you find the distance of Mahalanobis between them?

(I got some advice on using these remote measures on https://stackoverflow.com/a/299602/ ... myself, and there is a question on how to calculate the Cos similarity, so please consider before closing this question)

Answer 1

You must evaluate the covariance matrix.

Related Wikipedia articles this and this .

For multidimensional vectors (n observations of a p-dimensional variable), the formula for the Mahalanobis distance is

Where S is the inverse covariance matrix, which can be estimated as:

where is the ith observation of a (p-dimensional) random variable and

Be careful that using the Mahalanobis distance between your vectors only makes sense if all of your expected vector values ​​match.

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