{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T15:39:28Z","timestamp":1773329968261,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62006078"],"award-info":[{"award-number":["62006078"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62076096"],"award-info":[{"award-number":["62076096"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Municipal Project","award":["20511100900"],"award-info":[{"award-number":["20511100900"]}]},{"name":"Shanghai Knowledge Service Platform Project","award":["ZF1213"],"award-info":[{"award-number":["ZF1213"]}]},{"name":"Shanghai Chenguang Program","award":["19CG25"],"award-info":[{"award-number":["19CG25"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.<\/jats:p>","DOI":"10.3390\/e23101290","type":"journal-article","created":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T10:22:42Z","timestamp":1632997362000},"page":"1290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0158-5330","authenticated-orcid":false,"given":"Jing","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiliang","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiwei","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2407","DOI":"10.1016\/j.patcog.2015.02.028","article-title":"Modeling and recognizing human trajectories with beta process hidden Markov models","volume":"48","author":"Sun","year":"2015","journal-title":"Pattern Recognit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1109\/5.18626","article-title":"A tutorial on hidden Markov models and selected applications in speech recognition","volume":"77","author":"Rabiner","year":"1989","journal-title":"Proc. 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