{"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/diffred-dimensionality-reduction-guided-by","title":"DiffRed: Dimensionality Reduction guided by stable rank","arxiv_id":"2403.05882","date":"2024-03-09","proceeding":null,"authors":["Prarabdh Shukla","Gagan Raj Gupta","Kunal Dutta"],"abstract":"In this work, we propose a novel dimensionality reduction technique, DiffRed, which first projects the data matrix, A, along first $k_1$ principal components and the residual matrix $A^{*}$ (left after subtracting its $k_1$-rank approximation) along $k_2$ Gaussian random vectors. We evaluate M1, the distortion of mean-squared pair-wise distance, and Stress, the normalized value of RMS of distortion of the pairwise distances. We rigorously prove that DiffRed achieves a general upper bound of $O\\left(\\sqrt{\\frac{1-p}{k_2}}\\right)$ on Stress and $O\\left(\\frac{(1-p)}{\\sqrt{k_2*\\rho(A^{*})}}\\right)$ on M1 where $p$ is the fraction of variance explained by the first $k_1$ principal components and $\\rho(A^{*})$ is the stable rank of $A^{*}$. These bounds are tighter than the currently known results for Random maps. Our extensive experiments on a variety of real-world datasets demonstrate that DiffRed achieves near zero M1 and much lower values of Stress as compared to the well-known dimensionality reduction techniques. In particular, DiffRed can map a 6 million dimensional dataset to 10 dimensions with 54% lower Stress than PCA.","url_abs":"https://arxiv.org/abs/2403.05882v1","url_pdf":"https://arxiv.org/pdf/2403.05882v1.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":"diffred-dimensionality-reduction-guided-by","repo_url":"https://github.com/s3-lab-iit/diffred","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"data-summarization","task_name":"Data Summarization"},{"task_slug":"data-visualization","task_name":"Data Visualization"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}