{"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/tensor-canonical-correlation-analysis-for","title":"Tensor Canonical Correlation Analysis for Multi-view Dimension Reduction","arxiv_id":"1502.02330","date":"2015-02-09","proceeding":null,"authors":["Yong Luo","DaCheng Tao","Yonggang Wen","Kotagiri Ramamohanarao","Chao Xu"],"abstract":"Canonical correlation analysis (CCA) has proven an effective tool for\ntwo-view dimension reduction due to its profound theoretical foundation and\nsuccess in practical applications. In respect of multi-view learning, however,\nit is limited by its capability of only handling data represented by two-view\nfeatures, while in many real-world applications, the number of views is\nfrequently many more. Although the ad hoc way of simultaneously exploring all\npossible pairs of features can numerically deal with multi-view data, it\nignores the high order statistics (correlation information) which can only be\ndiscovered by simultaneously exploring all features.\n  Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly\nyet naturally generalizes CCA to handle the data of an arbitrary number of\nviews by analyzing the covariance tensor of the different views. TCCA aims to\ndirectly maximize the canonical correlation of multiple (more than two) views.\nCrucially, we prove that the multi-view canonical correlation maximization\nproblem is equivalent to finding the best rank-1 approximation of the data\ncovariance tensor, which can be solved efficiently using the well-known\nalternating least squares (ALS) algorithm. As a consequence, the high order\ncorrelation information contained in the different views is explored and thus a\nmore reliable common subspace shared by all features can be obtained. In\naddition, a non-linear extension of TCCA is presented. Experiments on various\nchallenge tasks, including large scale biometric structure prediction, internet\nadvertisement classification and web image annotation, demonstrate the\neffectiveness of the proposed method.","url_abs":"http://arxiv.org/abs/1502.02330v1","url_pdf":"http://arxiv.org/pdf/1502.02330v1.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":"tensor-canonical-correlation-analysis-for","repo_url":"https://github.com/basiralab/MV-LEAP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"tensor-canonical-correlation-analysis-for","repo_url":"https://github.com/jameschapman19/cca_zoo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"tensor-canonical-correlation-analysis-for","repo_url":"https://github.com/rciszek/mdr_tcca","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"multi-view-learning","task_name":"MULTI-VIEW LEARNING"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1502.02330","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}