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010   $a3-030-76974-7
024 7 $a10.1007/978-3-030-76974-1
035   $a(CKB)4100000012026586
035   $a(MiAaPQ)EBC6727046
035   $a(Au-PeEL)EBL6727046
035   $a(OCoLC)1268326111
035   $a(PPN)258054654
035   $a(DE-He213)978-3-030-76974-1
035   $a(EXLCZ)994100000012026586
100   $a20210915d2021      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aMultivariate Data Analysis on Matrix Manifolds $e(with Manopt) /$fby Nickolay Trendafilov, Michele Gallo
205   $a1st ed. 2021.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021.
215   $a1 online resource (467 pages)
225 1 $aSpringer Series in the Data Sciences,$x2365-5682
311 08$a3-030-76973-9 
327   $aIntroduction -- Matrix analysis and differentiation -- Matrix manifolds in MDA -- Principal component analysis (PCA) -- Factor analysis (FA) -- Procrustes analysis (PA) -- Linear discriminant analysis (LDA) -- Canonical correlation analysis (CCA) -- Common principal components (CPC) -- Metric multidimensional scaling (MDS) and related methods -- Data analysis on simplexes.
330   $aThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number ofexercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. .
410  0$aSpringer Series in the Data Sciences,$x2365-5682
606   $aMathematics$xData processing
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aComputer science$xMathematics
606   $aComputational Mathematics and Numerical Analysis
606   $aGlobal Analysis and Analysis on Manifolds
606   $aMathematical Applications in Computer Science
615  0$aMathematics$xData processing.
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615  0$aComputer science$xMathematics.
615 14$aComputational Mathematics and Numerical Analysis.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aMathematical Applications in Computer Science.
676   $a519.535
700   $aTrendafilov$b Nickolay$0848301
702   $aGallo$b Michele
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910502639203321
996   $aMultivariate data analysis on matrix manifolds$92880339
997   $aUNINA