{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-distance-for-hmms-based-on-aggregated","title":"A Distance for HMMs based on Aggregated Wasserstein Metric and State Registration","arxiv_id":"1608.01747","date":"2016-08-05","proceeding":null,"authors":["Yukun Chen","Jianbo Ye","Jia Li"],"abstract":"We propose a framework, named Aggregated Wasserstein, for computing a\ndissimilarity measure or distance between two Hidden Markov Models with state\nconditional distributions being Gaussian. For such HMMs, the marginal\ndistribution at any time spot follows a Gaussian mixture distribution, a fact\nexploited to softly match, aka register, the states in two HMMs. We refer to\nsuch HMMs as Gaussian mixture model-HMM (GMM-HMM). The registration of states\nis inspired by the intrinsic relationship of optimal transport and the\nWasserstein metric between distributions. Specifically, the components of the\nmarginal GMMs are matched by solving an optimal transport problem where the\ncost between components is the Wasserstein metric for Gaussian distributions.\nThe solution of the optimization problem is a fast approximation to the\nWasserstein metric between two GMMs. The new Aggregated Wasserstein distance is\na semi-metric and can be computed without generating Monte Carlo samples. It is\ninvariant to relabeling or permutation of the states. This distance quantifies\nthe dissimilarity of GMM-HMMs by measuring both the difference between the two\nmarginal GMMs and the difference between the two transition matrices. Our new\ndistance is tested on the tasks of retrieval and classification of time series.\nExperiments on both synthetic data and real data have demonstrated its\nadvantages in terms of accuracy as well as efficiency in comparison with\nexisting distances based on the Kullback-Leibler divergence.","url_abs":"http://arxiv.org/abs/1608.01747v1","url_pdf":"http://arxiv.org/pdf/1608.01747v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-distance-for-hmms-based-on-aggregated","repo_url":"https://github.com/cykustcc/aggregated_wasserstein_hmm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"retrieval","task_name":"Retrieval"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}