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This paper investigates an ordered partial matching alignment problem, in which the goal is to align two sequences in the presence of potentially non-matching regions. We propose a novel parameter-free dynamic programming alignment method called hidden state time warping that allows an alignment path to switch between two different planes: a “visible” plane corresponding to matching sections and a “hidden” plane corresponding to non-matching sections. By defining two distinct planes, we can allow different types of time warping in each plane (e.g., imposing a maximum warping factor in matching regions while allowing completely unconstrained movements in non-matching regions). The resulting algorithm can determine the optimal continuous alignment path via dynamic programming, and the visible plane induces a (possibly) discontinuous alignment path containing matching regions. We show that this approach outperforms existing parameter-free methods on two different partial matching alignment problems involving speech and music.