I have a list of k-dimensional features M. I want to find in this list the nearest item to a query feature A. Feature comparison is not directly based on a common metric (such as Euclidean or Symmetric Chi2). Rather, the comparison between feature A and feature B is done as follows : compute the distance (any common metric) between feature A and B’. B’ is obtained from circular shifting of B. Since the features are k-dimensional, we obtain k-1 distances between A and B, and the comparison function returns the lowest.
Considering my comparison function above, is it possible to optimize the NN search with an appropriate algorithm or data structure ?