{"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/parallelized-tensor-train-learning-of","title":"Parallelized Tensor Train Learning of Polynomial Classifiers","arxiv_id":"1612.06505","date":"2016-12-20","proceeding":null,"authors":["Zhongming Chen","Kim Batselier","Johan A. K. Suykens","Ngai Wong"],"abstract":"In pattern classification, polynomial classifiers are well-studied methods as\nthey are capable of generating complex decision surfaces. Unfortunately, the\nuse of multivariate polynomials is limited to kernels as in support vector\nmachines, because polynomials quickly become impractical for high-dimensional\nproblems. In this paper, we effectively overcome the curse of dimensionality by\nemploying the tensor train format to represent a polynomial classifier. Based\non the structure of tensor trains, two learning algorithms are proposed which\ninvolve solving different optimization problems of low computational\ncomplexity. Furthermore, we show how both regularization to prevent overfitting\nand parallelization, which enables the use of large training sets, are\nincorporated into these methods. Both the efficiency and efficacy of our\ntensor-based polynomial classifier are then demonstrated on the two popular\ndatasets USPS and MNIST.","url_abs":"http://arxiv.org/abs/1612.06505v4","url_pdf":"http://arxiv.org/pdf/1612.06505v4.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":"parallelized-tensor-train-learning-of","repo_url":"https://github.com/kbatseli/TTClassifier","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"LGPL-3.0"}}],"tasks":[{"task_slug":"classification","task_name":"General Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.06505","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}