{"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/linear-dimensionality-reduction-survey","title":"Linear Dimensionality Reduction: Survey, Insights, and Generalizations","arxiv_id":"1406.0873","date":"2014-06-03","proceeding":null,"authors":["John P. Cunningham","Zoubin Ghahramani"],"abstract":"Linear dimensionality reduction methods are a cornerstone of analyzing high\ndimensional data, due to their simple geometric interpretations and typically\nattractive computational properties. These methods capture many data features\nof interest, such as covariance, dynamical structure, correlation between data\nsets, input-output relationships, and margin between data classes. Methods have\nbeen developed with a variety of names and motivations in many fields, and\nperhaps as a result the connections between all these methods have not been\nhighlighted. Here we survey methods from this disparate literature as\noptimization programs over matrix manifolds. We discuss principal component\nanalysis, factor analysis, linear multidimensional scaling, Fisher's linear\ndiscriminant analysis, canonical correlations analysis, maximum autocorrelation\nfactors, slow feature analysis, sufficient dimensionality reduction,\nundercomplete independent component analysis, linear regression, distance\nmetric learning, and more. This optimization framework gives insight to some\nrarely discussed shortcomings of well-known methods, such as the suboptimality\nof certain eigenvector solutions. Modern techniques for optimization over\nmatrix manifolds enable a generic linear dimensionality reduction solver, which\naccepts as input data and an objective to be optimized, and returns, as output,\nan optimal low-dimensional projection of the data. This simple optimization\nframework further allows straightforward generalizations and novel variants of\nclassical methods, which we demonstrate here by creating an\northogonal-projection canonical correlations analysis. More broadly, this\nsurvey and generic solver suggest that linear dimensionality reduction can move\ntoward becoming a blackbox, objective-agnostic numerical technology.","url_abs":"http://arxiv.org/abs/1406.0873v2","url_pdf":"http://arxiv.org/pdf/1406.0873v2.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":"linear-dimensionality-reduction-survey","repo_url":"https://github.com/cunni/ldr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"metric-learning","task_name":"Metric Learning"},{"task_slug":"survey","task_name":"Survey"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}