{"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/shape-constrained-tensor-decompositions-using","title":"Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Libraries","arxiv_id":"1608.04674","date":"2016-08-16","proceeding":null,"authors":["Bethany Lusch","Eric C. Chi","J. Nathan Kutz"],"abstract":"We consider $N$-way data arrays and low-rank tensor factorizations where the\ntime mode is coded as a sparse linear combination of temporal elements from an\nover-complete library. Our method, Shape Constrained Tensor Decomposition\n(SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces\n$r$-rank approximations of data tensors via outer products of vectors in each\ndimension of the data. By constraining the vector in the temporal dimension to\nknown analytic forms which are selected from a large set of candidate\nfunctions, more readily interpretable decompositions are achieved and analytic\ntime dependencies discovered. The SCTD method circumvents traditional {\\em\nflattening} techniques where an $N$-way array is reshaped into a matrix in\norder to perform a singular value decomposition. A clear advantage of the SCTD\nalgorithm is its ability to extract transient and intermittent phenomena which\nis often difficult for SVD-based methods. We motivate the SCTD method using\nseveral intuitively appealing results before applying it on a number of\nhigh-dimensional, real-world data sets in order to illustrate the efficiency of\nthe algorithm in extracting interpretable spatio-temporal modes. With the rise\nof data-driven discovery methods, the decomposition proposed provides a viable\ntechnique for analyzing multitudes of data in a more comprehensible fashion.","url_abs":"http://arxiv.org/abs/1608.04674v1","url_pdf":"http://arxiv.org/pdf/1608.04674v1.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":"shape-constrained-tensor-decompositions-using","repo_url":"https://github.com/BethanyL/SCTD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}