{"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/a-pca-like-autoencoder","title":"A PCA-like Autoencoder","arxiv_id":"1904.01277","date":"2019-04-02","proceeding":null,"authors":["Saïd Ladjal","Alasdair Newson","Chi-Hieu Pham"],"abstract":"An autoencoder is a neural network which data projects to and from a lower\ndimensional latent space, where this data is easier to understand and model.\nThe autoencoder consists of two sub-networks, the encoder and the decoder,\nwhich carry out these transformations. The neural network is trained such that\nthe output is as close to the input as possible, the data having gone through\nan information bottleneck : the latent space. This tool bears significant\nressemblance to Principal Component Analysis (PCA), with two main differences.\nFirstly, the autoencoder is a non-linear transformation, contrary to PCA, which\nmakes the autoencoder more flexible and powerful. Secondly, the axes found by a\nPCA are orthogonal, and are ordered in terms of the amount of variability which\nthe data presents along these axes. This makes the interpretability of the PCA\nmuch greater than that of the autoencoder, which does not have these\nattributes. Ideally, then, we would like an autoencoder whose latent space\nconsists of independent components, ordered by decreasing importance to the\ndata. In this paper, we propose an algorithm to create such a network. We\ncreate an iterative algorithm which progressively increases the size of the\nlatent space, learning a new dimension at each step. Secondly, we propose a\ncovariance loss term to add to the standard autoencoder loss function, as well\nas a normalisation layer just before the latent space, which encourages the\nlatent space components to be statistically independent. We demonstrate the\nresults of this autoencoder on simple geometric shapes, and find that the\nalgorithm indeed finds a meaningful representation in the latent space. This\nmeans that subsequent interpolation in the latent space has meaning with\nrespect to the geometric properties of the images.","url_abs":"http://arxiv.org/abs/1904.01277v1","url_pdf":"http://arxiv.org/pdf/1904.01277v1.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":"a-pca-like-autoencoder","repo_url":"https://github.com/chieupham/PCAAE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"interpretability","method_name":"Interpretability"},{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}