Canonical Soft Time Warping

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Keisuke Kawano, Satoshi Koide, Takuro Kutsuna ;
Proceedings of The Eleventh Asian Conference on Machine Learning, PMLR 101:551-566, 2019.

Abstract

Alignment of two given sequences (i.e., computing correspondence between frames considering local time shifting) is a fundamental operation for various applications such as computer vision and bioinformatics. To obtain an alignment between high-dimensional sequences, several methods have been proposed, including canonical time warping (CTW). However, the optimization problem for CTW, and its extensions, often fall into poor local minima when the initial solution is far from the global optima. In this paper, we propose \emph{canonical soft time warping (CSTW)} in which an alignment is modeled as a probabilistic variable that follows the Gibbs distribution with temperature $\gamma$. We also propose the annealing CSTW (ACTW), a variant of CSTW that gradually decreases $\gamma$. ACTW is useful when underlying applications require hard alignments. Using synthetic and real-world data, we experimentally demonstrate that our proposed methods outperform previous methods, including CTW, in estimating alignments. In particular, our method does not suffer from poor local minima, as a consequence of the probabilistic treatment of alignments.

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