0376327 20240111140815.720120911235959.9 10.1007/978-3-642-28551-6_37 9 s. C cav_un_epca*0376325978-3-642-28550-9297-305HeidelbergSpringer2012TheisFabian tensor decomposition pattern analysis structural complexity cav_un_auth*0274170 Phan A. H. JP cav_un_auth*0272321 Cichocki A. JP cav_un_auth*0101212 Tichavský Petr Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0208388 Mandic D. GB cav_un_auth*0214972 Matsuoka K. JP http://library.utia.cas.cz/separaty/2012/SI/tichavsky-on revealing replicating structures in multiway data a novel tensor decomposition approach.pdf 533kB GA102/09/1278 GA ČR cav_un_auth*0253174 A novel tensor decomposition is proposed to make it possible to identify replicating structures in complex data, such as textures and patterns in music spectrograms. In order to establish a computational framework for this paradigm, we adopt a multiway (tensor) approach. To this end, a novel tensor product is introduced, and the subsequent analysis of its properties shows a perfect match to the task of identification of recurrent structures present in the data. Out of a whole class of possible algorithms, we illuminate those derived so as to cater for orthogonal and nonnegative patterns. Simulations on texture images and a complex music sequence confirm the benefits of the proposed model and of the associated learning algorithms. cav_un_auth*0280771 Latent Variable Analysis and Signal Separation,10th International Conference, LVA/ICA 2012 Tel Aviv 12.03.2012-15.03.2012 IL 2013 BB 5 PR RVO:67985556 http://hdl.handle.net/11104/0208757 2012 533kB cav_un_epca*0376325 Latent Variable Analysis and Signal Separation 978-3-642-28550-9 297 305 Heidelberg Springer 2012 Lecture Notes on Computer Science 7191 Theis Fabian 340