  We propose to learn multiple local Mahalanobis distance metrics to perform
k-nearest neighbor (kNN) classification of temporal sequences. Temporal
sequences are first aligned by dynamic time warping (DTW); given the alignment
path, similarity between two sequences is measured by the DTW distance, which
is computed as the accumulated distance between matched temporal point pairs
along the alignment path. Traditionally, Euclidean metric is used for distance
computation between matched pairs, which ignores the data regularities and
might not be optimal for applications at hand. Here we propose to learn
multiple Mahalanobis metrics, such that DTW distance becomes the sum of
Mahalanobis distances. We adapt the large margin nearest neighbor (LMNN)
framework to our case, and formulate multiple metric learning as a linear
programming problem. Extensive sequence classification results show that our
proposed multiple metrics learning approach is effective, insensitive to the
preceding alignment qualities, and reaches the state-of-the-art performances on
UCR time series datasets.
