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010   $a978-30-307-6976-5
100   $a20240216d2021       |0itac50      ba
101   $aeng
102   $aCH
105   $a||||    |||||
200 1 $aMultivariate data analysis on matrix manifolds (with Manopt)$fNickolay Trendafilov, Michele Gallo
210   $aCham$eCH$cSpringer$d2021
215   $aXX, 450 p.$d23 cm.
330   $aThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number ofexercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.
410  1$1001UON00523850$12001 $aSpringer series in the Data Sciences.
606   $aAnalisi multivariata$xMetodi$3UONC034747$2FI
606   $aAnalisi statistica multivariata$3UONC034757$2FI
606   $aStatistica matematica$3UONC039315$2FI
620   $aCH$dCham$3UONL005304
676   $a310$cStatistica$v21
700  1$aTrendafilov$bNickolay$3UONV295139$0848301
701  1$aGallo$bMichele$3UONV295138$0497553
712   $aSpringer$3UONV283843$4650
801   $aIT$bSOL$c20250711$gRICA
899   $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI
912   $aUON00523088
950   $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI 2.0                                 0540                $eSI    50930    5        0540                $sBuono
951   $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$bSI2024200       1J                   20240216Bolla n. 55 del 14.3.2024.                                                      
996   $aMultivariate Data Analysis on Matrix Manifolds$94153349
997   $aUNIOR