{"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/12071230","title":"Higher-Order Partial Least Squares (HOPLS): A Generalized Multi-Linear Regression Method","arxiv_id":"1207.1230","date":"2012-07-05","proceeding":null,"authors":["Qibin Zhao","Cesar F. Caiafa","Danilo P. Mandic","Zenas C. Chao","Yasuo Nagasaka","Naotaka Fujii","Liqing Zhang","Andrzej Cichocki"],"abstract":"A new generalized multilinear regression model, termed the Higher-Order\nPartial Least Squares (HOPLS), is introduced with the aim to predict a tensor\n(multiway array) $\\tensor{Y}$ from a tensor $\\tensor{X}$ through projecting the\ndata onto the latent space and performing regression on the corresponding\nlatent variables. HOPLS differs substantially from other regression models in\nthat it explains the data by a sum of orthogonal Tucker tensors, while the\nnumber of orthogonal loadings serves as a parameter to control model complexity\nand prevent overfitting. The low dimensional latent space is optimized\nsequentially via a deflation operation, yielding the best joint subspace\napproximation for both $\\tensor{X}$ and $\\tensor{Y}$. Instead of decomposing\n$\\tensor{X}$ and $\\tensor{Y}$ individually, higher order singular value\ndecomposition on a newly defined generalized cross-covariance tensor is\nemployed to optimize the orthogonal loadings. A systematic comparison on both\nsynthetic data and real-world decoding of 3D movement trajectories from\nelectrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the\nexisting methods in terms of better predictive ability, suitability to handle\nsmall sample sizes, and robustness to noise.","url_abs":"http://arxiv.org/abs/1207.1230v1","url_pdf":"http://arxiv.org/pdf/1207.1230v1.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":"12071230","repo_url":"https://github.com/arthurdehgan/HOPLS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}