{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T23:06:42Z","timestamp":1676848002359},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Neur. Syst."],"published-print":{"date-parts":[[2004,10]]},"abstract":"<jats:p> Principal Component Analysis (PCA) and Principal Subspace Analysis (PSA) are classic techniques in statistical data analysis, feature extraction and data compression. Given a set of multivariate measurements, PCA and PSA provide a smaller set of \"basis vectors\" with less redundancy, and a subspace spanned by them, respectively. Artificial neurons and neural networks have been shown to perform PSA and PCA when gradient ascent (descent) learning rules are used, which is related to the constrained maximization (minimization) of statistical objective functions. Due to their low complexity, such algorithms and their implementation in neural networks are potentially useful in cases of tracking slow changes of correlations in the input data or in updating eigenvectors with new samples. In this paper we propose PCA learning algorithm that is fully homogeneous with respect to neurons. The algorithm is obtained by modification of one of the most famous PSA learning algorithms \u2014 Subspace Learning Algorithm (SLA). Modification of the algorithm is based on Time-Oriented Hierarchical Method (TOHM). The method uses two distinct time scales. On a faster time scale PSA algorithm is responsible for the \"behavior\" of all output neurons. On a slower scale, output neurons will compete for fulfilment of their \"own interests\". On this scale, basis vectors in the principal subspace are rotated toward the principal eigenvectors. At the end of the paper it will be briefly analyzed how (or why) time-oriented hierarchical method can be used for transformation of any of the existing neural network PSA method, into PCA method. <\/jats:p>","DOI":"10.1142\/s0129065704002091","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T22:29:42Z","timestamp":1101248982000},"page":"313-323","source":"Crossref","is-referenced-by-count":6,"title":["TIME-ORIENTED HIERARCHICAL METHOD FOR COMPUTATION OF PRINCIPAL COMPONENTS USING SUBSPACE LEARNING ALGORITHM"],"prefix":"10.1142","volume":"14","author":[{"given":"MARKO","family":"JANKOVIC","sequence":"first","affiliation":[{"name":"Control Department, Electrical Engineering Institute \"Nikola Tesla\", Koste Glavinica 8a, 11000 Belgrade, Serbia, Serbia and Montenegro"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HIDEMITSU","family":"OGAWA","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Tokyo Institute of Technology, Tokyo, 152-8552, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/72.392248"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/72.839005"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/72.655030"},{"key":"rf4","volume-title":"Adaptive Blind Signal and Image Processing \u2014 Learning Algorithms and Applications","author":"Chichocki A.","year":"2003"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4016-7"},{"key":"rf6","unstructured":"K. I.\u00a0Diamantaras, ICNN'96 (1996)\u00a0pp. 74\u201377."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/97.735427"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895290954"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1162\/089976601750265036"},{"key":"rf10","first-page":"334","volume":"6","author":"Fyfe C.","journal-title":"Network: Computation in Neural Systems"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00199896"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.813836"},{"key":"rf14","first-page":"215","volume":"3","author":"Jankovic M.","journal-title":"Int. J. Neural Systems"},{"key":"rf15","volume-title":"Principles of Power Electronics","author":"Kassakian J. G.","year":"1991"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1977.1101561"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275687"},{"key":"rf19","volume-title":"Subspace Method of Pattern Recognition","author":"Oja E.","year":"1983"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1142\/S0129065789000475"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(85)90131-3"},{"key":"rf22","first-page":"366","volume":"75","author":"Oja E.","journal-title":"IEICE Trans. Inf. & Syst."},{"key":"rf23","first-page":"376","volume":"75","author":"Oja E.","journal-title":"IEICE Trans. Inf. & Syst."},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1109\/72.822524"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1109\/72.508948"},{"key":"rf26","volume":"78","author":"Plumbley M.","journal-title":"Technical Report CUED\/F-INFENG\/TR."},{"key":"rf27","first-page":"1242","volume":"11","author":"Weingessel A.","journal-title":"IEEE Trans. on Neural Networks"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80107-8"},{"key":"rf29","first-page":"674","volume":"5","author":"Yan W.","journal-title":"IEEE Trans. on Neural Networks"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1109\/72.839022"}],"container-title":["International Journal of Neural Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129065704002091","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:07:33Z","timestamp":1565129253000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129065704002091"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":28,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1142\/S0129065704002091"],"URL":"https:\/\/doi.org\/10.1142\/s0129065704002091","relation":{},"ISSN":["0129-0657","1793-6462"],"issn-type":[{"value":"0129-0657","type":"print"},{"value":"1793-6462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}