{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T05:52:36Z","timestamp":1698213156458},"reference-count":25,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":5192,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp;amp; Computers in Japan"],"published-print":{"date-parts":[[1993,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a systematic discussion of the relationship between classical multivariate analysis and various data compression methods arising from the nonlinear mapping capability of multilayer neural networks. The important points of a geometrical interpretation for the case of four or more layers are set down using the well known autoassociation model and the pulse\u2010input\/pattern\u2010output network (PPN) model proposed by the authors. Next, the previously unused four\u2010layer autoassociative model is investigated and its effectiveness is demonstrated. Then, the four\u2010layer autoassociative mapping model and the four\u2010layer PPN are compared using a method based on multivariate analysis. That is, it is shown that each method can be related in an approximate fashion to piecewise\u2010linear data compression models as well as to factor analysis models. Finally, to back up these studies, several example experiments are described; a five\u2010layer autoassociative mapping model is then examined, and the data compression capabilities of all three models are compared.<\/jats:p>","DOI":"10.1002\/scj.4690240103","type":"journal-article","created":{"date-parts":[[2007,7,8]],"date-time":"2007-07-08T00:13:45Z","timestamp":1183853625000},"page":"28-46","source":"Crossref","is-referenced-by-count":0,"title":["Analysis of the data concentration function of a four\u2010layer neural network in terms of the autoassociation and PPN models"],"prefix":"10.1002","volume":"24","author":[{"given":"Tatsuhiro","family":"Yonekura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin\u2010Ya","family":"Miyazaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun\u2010Ichiro","family":"Toriwaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/5236.001.0001"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00332918"},{"issue":"1","key":"e_1_2_1_4_2","first-page":"139","article-title":"A theoretical study of the approximate representations of autoassociative mappings using three\u2010layer neural networks","volume":"73","author":"Funahashi K.","year":"1990","journal-title":"Trans. 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