Learning Distance for Sequences by Learning a Ground Metric

Most existing metric learning methods are developed for vector representations. Learning distances that operate directly on multi-dimensional sequences is challenging because such distances are structural by nature and the vectors in sequences are not independent. Generally, distances for sequences heavily depend on the ground metric between the vectors in sequences. We propose to learn the distance for sequences through learning a ground Mahalanobis metric for the vectors in sequences. The learning samples are sequences of vectors for which how the ground metric between vectors induces the overall distance is given. The objective is that the distance induced by the learned ground metric affects large values for sequences from different classes and small values for those from the same class. We formulate the metric as a parameter of the distance and bring closer each sequence to an associated virtual sequence w.r.t. the distance to reduce the number of constraints. We develop a general iterative solution for any ground-metric-based sequence distance. Experiments on several sequence datasets demonstrate the effectiveness and efficiency of our method.