{"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/dimensionality-reduction-for-binary-data","title":"Dimensionality Reduction for Binary Data through the Projection of Natural Parameters","arxiv_id":"1510.06112","date":"2015-10-21","proceeding":null,"authors":["Andrew J. Landgraf","Yoonkyung Lee"],"abstract":"Principal component analysis (PCA) for binary data, known as logistic PCA,\nhas become a popular alternative to dimensionality reduction of binary data. It\nis motivated as an extension of ordinary PCA by means of a matrix\nfactorization, akin to the singular value decomposition, that maximizes the\nBernoulli log-likelihood. We propose a new formulation of logistic PCA which\nextends Pearson's formulation of a low dimensional data representation with\nminimum error to binary data. Our formulation does not require a matrix\nfactorization, as previous methods do, but instead looks for projections of the\nnatural parameters from the saturated model. Due to this difference, the number\nof parameters does not grow with the number of observations and the principal\ncomponent scores on new data can be computed with simple matrix multiplication.\nWe derive explicit solutions for data matrices of special structure and provide\ncomputationally efficient algorithms for solving for the principal component\nloadings. Through simulation experiments and an analysis of medical diagnoses\ndata, we compare our formulation of logistic PCA to the previous formulation as\nwell as ordinary PCA to demonstrate its benefits.","url_abs":"http://arxiv.org/abs/1510.06112v1","url_pdf":"http://arxiv.org/pdf/1510.06112v1.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":"dimensionality-reduction-for-binary-data","repo_url":"https://github.com/andland/logisticpca","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1510.06112","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}