{"title":"非线性系统的主成分分析:初步结果","authors":"B. Moore","doi":"10.1109/CDC.1979.270114","DOIUrl":null,"url":null,"abstract":"Principal component analysis (Hotelling, 1933), supported by the \"state of the art\" algorithm (Golub and Reinsch, 1970) for performing singular valud decomposition, is a powerful tool which has been applied (Moore, 1979) successfully in the analysis of linear systems. In this paper attention is called to the fact that it is also a very useful tool for computing and evaluating affine approximations of multi-dimensional nonlinear maps over specified domains. Included are preliminary ideas about application of the tool to the following problems: numerical linearization of dynamic systems, gradient approximations for optimization, and numerical differentiation of vector time signals.","PeriodicalId":338908,"journal":{"name":"1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1979-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Principal component analysis in nonlinear systems: Preliminary results\",\"authors\":\"B. Moore\",\"doi\":\"10.1109/CDC.1979.270114\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Principal component analysis (Hotelling, 1933), supported by the \\\"state of the art\\\" algorithm (Golub and Reinsch, 1970) for performing singular valud decomposition, is a powerful tool which has been applied (Moore, 1979) successfully in the analysis of linear systems. In this paper attention is called to the fact that it is also a very useful tool for computing and evaluating affine approximations of multi-dimensional nonlinear maps over specified domains. Included are preliminary ideas about application of the tool to the following problems: numerical linearization of dynamic systems, gradient approximations for optimization, and numerical differentiation of vector time signals.\",\"PeriodicalId\":338908,\"journal\":{\"name\":\"1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.1979.270114\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1979.270114","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Principal component analysis in nonlinear systems: Preliminary results
Principal component analysis (Hotelling, 1933), supported by the "state of the art" algorithm (Golub and Reinsch, 1970) for performing singular valud decomposition, is a powerful tool which has been applied (Moore, 1979) successfully in the analysis of linear systems. In this paper attention is called to the fact that it is also a very useful tool for computing and evaluating affine approximations of multi-dimensional nonlinear maps over specified domains. Included are preliminary ideas about application of the tool to the following problems: numerical linearization of dynamic systems, gradient approximations for optimization, and numerical differentiation of vector time signals.
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