{"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/an-online-riemannian-pca-for-stochastic","title":"An Online Riemannian PCA for Stochastic Canonical Correlation Analysis","arxiv_id":"2106.07479","date":"2021-06-08","proceeding":"NeurIPS 2021 12","authors":["Zihang Meng","Rudrasis Chakraborty","Vikas Singh"],"abstract":"We present an efficient stochastic algorithm (RSG+) for canonical correlation analysis (CCA) using a reparametrization of the projection matrices. We show how this reparametrization (into structured matrices), simple in hindsight, directly presents an opportunity to repurpose/adjust mature techniques for numerical optimization on Riemannian manifolds. Our developments nicely complement existing methods for this problem which either require $O(d^3)$ time complexity per iteration with $O(\\frac{1}{\\sqrt{t}})$ convergence rate (where $d$ is the dimensionality) or only extract the top $1$ component with $O(\\frac{1}{t})$ convergence rate. In contrast, our algorithm offers a strict improvement for this classical problem: it achieves $O(d^2k)$ runtime complexity per iteration for extracting the top $k$ canonical components with $O(\\frac{1}{t})$ convergence rate. While the paper primarily focuses on the formulation and technical analysis of its properties, our experiments show that the empirical behavior on common datasets is quite promising. We also explore a potential application in training fair models where the label of protected attribute is missing or otherwise unavailable.","url_abs":"https://arxiv.org/abs/2106.07479v1","url_pdf":"https://arxiv.org/pdf/2106.07479v1.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":"an-online-riemannian-pca-for-stochastic","repo_url":"https://github.com/zihangm/riemannian-streaming-cca","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"2k","task_name":"2k"},{"task_slug":"attribute","task_name":"Attribute"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2106.07479","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2106.07479"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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