Arvind Agarwal, J. M. Phillips, Suresh Venkatasubramanian
{"title":"通用多维标度","authors":"Arvind Agarwal, J. M. Phillips, Suresh Venkatasubramanian","doi":"10.1145/1835804.1835948","DOIUrl":null,"url":null,"abstract":"In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/µ2) log n)-dimensional sphere causes only an eps-distortion in the geodesic distances.","PeriodicalId":20529,"journal":{"name":"Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":"{\"title\":\"Universal multi-dimensional scaling\",\"authors\":\"Arvind Agarwal, J. M. Phillips, Suresh Venkatasubramanian\",\"doi\":\"10.1145/1835804.1835948\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/µ2) log n)-dimensional sphere causes only an eps-distortion in the geodesic distances.\",\"PeriodicalId\":20529,\"journal\":{\"name\":\"Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"32\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1835804.1835948\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1835804.1835948","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/µ2) log n)-dimensional sphere causes only an eps-distortion in the geodesic distances.