I am currently struggeling in a mixture of understanding the english meaning of component-wise vector comparison in the case of using the mahalanobis distance.
The comparison definition is: $$ b = \begin{cases} 0 &\mbox{if } x < y \\ 1 & \mbox{if } x \geq y \end{cases} $$
where x and y are vectors with the same dimension.
It is said that the comparison is done component-wise and using the mahalanobis distance.
From what I understand is, that I can calculate the norm of x and the norm of y, making it possible to decide wether x is smaller or greater than y.
Thinking about component-wise, this is to me to use every component in the vector x and compare it against the component in y. So for dimension 39 I would do 39 comparisons. But why should I need mahalanobis distance than?
Quote: "The equation performs a component-wise comparison between the user-specific vector x, estimated during the enrollment of the user, and a user-independent vector y (same for every user)"
Maybe I do misunderstand the part of component-wise comparison.
Note: Even that there is no word of mahalanobis, the rest of the text says that comparison is done using mahalanobis distance.