  To classify time series by nearest neighbors, we need to specify or learn one
or several distance measures. We consider variations of the Mahalanobis
distance measures which rely on the inverse covariance matrix of the data.
Unfortunately --- for time series data --- the covariance matrix has often low
rank. To alleviate this problem we can either use a pseudoinverse, covariance
shrinking or limit the matrix to its diagonal. We review these alternatives and
benchmark them against competitive methods such as the related Large Margin
Nearest Neighbor Classification (LMNN) and the Dynamic Time Warping (DTW)
distance. As we expected, we find that the DTW is superior, but the Mahalanobis
distance measures are one to two orders of magnitude faster. To get best
results with Mahalanobis distance measures, we recommend learning one distance
measure per class using either covariance shrinking or the diagonal approach.
