{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:22:37Z","timestamp":1648966957822},"reference-count":36,"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":[[2003,10]]},"abstract":"<jats:p> In previous contributions we presented a new class of algorithms for orthonormal learning of a linear neural network with p inputs and m outputs, based on the equations describing the dynamics of a massive rigid frame in a submanifold of \u211b<jats:sup>p<\/jats:sup>. While exhibiting interesting features, such as intrinsic numerical stability, strongly binding to the orthonormal submanifolds, and good controllability of the learning dynamics, tested on principal\/independent component analysis, the proposed algorithms were not completely satisfactory from a computational-complexity point of view. The main drawback was the need to repeatedly evaluate a matrix exponential map. With the aim to lessen the computational efforts pertaining to these algorithms, we propose here an improvement based on the closed-form Rodriguez formula for the exponential map. Such formula is available in the p=3 and m=3 case, which is discussed with details here. In particular, experimental results on independent component analysis (ICA), carried out with both synthetic and real-world data, help confirming the computational gain due to the proposed improvement. <\/jats:p>","DOI":"10.1142\/s0129065703001625","type":"journal-article","created":{"date-parts":[[2003,11,24]],"date-time":"2003-11-24T04:26:19Z","timestamp":1069647979000},"page":"273-290","source":"Crossref","is-referenced-by-count":3,"title":["STIEFEL-MANIFOLD LEARNING BY IMPROVED  RIGID-BODY THEORY APPLIED TO ICA"],"prefix":"10.1142","volume":"13","author":[{"given":"SIMONE","family":"FIORI","sequence":"first","affiliation":[{"name":"Faculty of Engineering, University of Perugia, Polo Didattico e Scientifico del Ternano, Loc. 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