{"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/statistically-motivated-second-order-pooling","title":"Statistically-motivated Second-order Pooling","arxiv_id":null,"date":"2018-09-01","proceeding":"ECCV 2018 9","authors":["Kaicheng Yu","Mathieu Salzmann "],"abstract":"However, the nature of such operations is usually computationally expensive, and resulting vector representation orders of magnitude larger than first-order baselines. Here, by contrast, we introduce a statistically-motivated framework that projects the second-order descriptor into a compact vector while improving the representational power.  To this end, we design a parametric vectorization layer, which maps a covariance matrix, known to follow a Wishart distribution, to a vector whose elements can be shown to follow a Chi-square distribution. We then propose to make use of a square-root normalization, which makes the distribution of the resulting representation converge to a Gaussian, with which most classifiers of recent first-order networks complying. As evidenced by our experiments, this lets us outperform the state-of-the-art first-order and second-order models on several benchmark recognition datasets.","url_abs":"http://openaccess.thecvf.com/content_ECCV_2018/html/Kaicheng_Yu_Statistically-motivated_Second-order_Pooling_ECCV_2018_paper.html","url_pdf":"http://openaccess.thecvf.com/content_ECCV_2018/papers/Kaicheng_Yu_Statistically-motivated_Second-order_Pooling_ECCV_2018_paper.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":"statistically-motivated-second-order-pooling","repo_url":"https://github.com/kcyu2014/smsop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}