{"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/from-principal-subspaces-to-principal","title":"From Principal Subspaces to Principal Components with Linear Autoencoders","arxiv_id":"1804.10253","date":"2018-04-26","proceeding":null,"authors":["Elad Plaut"],"abstract":"The autoencoder is an effective unsupervised learning model which is widely\nused in deep learning. It is well known that an autoencoder with a single\nfully-connected hidden layer, a linear activation function and a squared error\ncost function trains weights that span the same subspace as the one spanned by\nthe principal component loading vectors, but that they are not identical to the\nloading vectors. In this paper, we show how to recover the loading vectors from\nthe autoencoder weights.","url_abs":"http://arxiv.org/abs/1804.10253v3","url_pdf":"http://arxiv.org/pdf/1804.10253v3.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":"from-principal-subspaces-to-principal","repo_url":"https://github.com/plaut/linear-ae-pca","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1804.10253","atlas_url":"https://app.syntology.ai/?focus=1804.10253","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}