{"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/transform-invariant-non-parametric-clustering","title":"Transform-Invariant Non-Parametric Clustering of Covariance Matrices and its Application to Unsupervised Joint Segmentation and Action Discovery","arxiv_id":"1710.10060","date":"2017-10-27","proceeding":null,"authors":["Nadia Figueroa","Aude Billard"],"abstract":"In this work, we tackle the problem of transform-invariant unsupervised\nlearning in the space of Covariance matrices and applications thereof. We begin\nby introducing the Spectral Polytope Covariance Matrix (SPCM) Similarity\nfunction; a similarity function for Covariance matrices, invariant to any type\nof transformation. We then derive the SPCM-CRP mixture model, a\ntransform-invariant non-parametric clustering approach for Covariance matrices\nthat leverages the proposed similarity function, spectral embedding and the\ndistance-dependent Chinese Restaurant Process (dd-CRP) (Blei and Frazier,\n2011). The scalability and applicability of these two contributions is\nextensively validated on real-world Covariance matrix datasets from diverse\nresearch fields. Finally, we couple the SPCM-CRP mixture model with the\nBayesian non-parametric Indian Buffet Process (IBP) - Hidden Markov Model (HMM)\n(Fox et al., 2009), to jointly segment and discover transform-invariant action\nprimitives from complex sequential data. Resulting in a topic-modeling inspired\nhierarchical model for unsupervised time-series data analysis which we call\nICSC-HMM (IBP Coupled SPCM-CRP Hidden Markov Model). The ICSC-HMM is validated\non kinesthetic demonstrations of uni-manual and bi-manual cooking tasks;\nachieving unsupervised human-level decomposition of complex sequential tasks.","url_abs":"http://arxiv.org/abs/1710.10060v1","url_pdf":"http://arxiv.org/pdf/1710.10060v1.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":"transform-invariant-non-parametric-clustering","repo_url":"https://github.com/nbfigueroa/ICSC-HMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"transform-invariant-non-parametric-clustering","repo_url":"https://github.com/nbfigueroa/SPCM-CRP","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}