Learning Low-Dimensional Temporal Representations with Latent Alignments

Low-dimensional discriminative representations enhance machine learning methods in both performance and complexity. This has motivated supervised dimensionality reduction (DR), which transforms high-dimensional data into a discriminative subspace. Most DR methods require data to be i.i.d. However, in some domains, data naturally appear in sequences, where the observations are temporally correlated. We propose a DR method, namely, latent temporal linear discriminant analysis (LT-LDA), to learn low-dimensional temporal representations. We construct the separability among sequence classes by lifting the holistic temporal structures, which are established based on temporal alignments and may change in different subspaces. We jointly learn the subspace and the associated latent alignments by optimizing an objective that favors easily separable temporal structures. We show that this objective is connected to the inference of alignments and thus allows for an iterative solution. We provide both theoretical insight and empirical evaluations on several real-world sequence datasets to show the applicability of our method.