LEADER 04154nam 22006135 450 001 9910254078403321 005 20251116145709.0 010 $a4-431-55387-8 024 7 $a10.1007/978-4-431-55387-8 035 $a(CKB)3710000000588340 035 $a(EBL)4388673 035 $a(SSID)ssj0001653992 035 $a(PQKBManifestationID)16433921 035 $a(PQKBTitleCode)TC0001653992 035 $a(PQKBWorkID)14982545 035 $a(PQKB)10426112 035 $a(DE-He213)978-4-431-55387-8 035 $a(MiAaPQ)EBC4388673 035 $a(PPN)192219901 035 $a(EXLCZ)993710000000588340 100 $a20160202d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied matrix and tensor variate data analysis /$fedited by Toshio Sakata 205 $a1st ed. 2016. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2016. 215 $a1 online resource (144 p.) 225 1 $aJSS Research Series in Statistics,$x2364-0057 300 $aDescription based upon print version of record. 311 08$a4-431-55386-X 320 $aIncludes bibliographical references at the end of each chapters. 327 $a1 Three-Way Principal Component Analysis with its Applications to Psychology (Kohei Adachi) -- 2 Non-negative matrix factorization and its variants for audio signal processing (Hirokazu Kameoka) -- 3 Generalized Tensor PCA and its Applications to Image Analysis (Kohei Inoue) -- 4 Matrix Factorization for Image Processing (Noboru Murata) -- 5 Arrays Normal Model and Incomplete Array Variate Observations (Deniz Akdemir) -- 6 One-sided Tests for Matrix Variate Normal Distribution (Manabu Iwasa and Toshio Sakata). 330 $aThis book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to be extremely useful for recently emerging complex and high-dimensional data in various applied fields. The reviews contained herein cover recent applications of these methods in psychology (Chap. 1), audio signals (Chap. 2) , image analysis  from tensor principal component analysis (Chap. 3), and image analysis from decomposition (Chap. 4), and genetic data (Chap. 5) . Readers will be able to understand the present status of these techniques as applicable to their own fields.  In Chapter 5 especially, a theory of tensor normal distributions, which is a basic in statistical inference, is developed, and multi-way regression, classification, clustering, and principal component analysis are exemplified under tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate and tensor variate normal distributions, whose theory under multivariate normal distributions has been a popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al. (1988). Chapters 1, 5, and 6 distinguish this book from ordinary engineering books on these topics. 410 0$aJSS Research Series in Statistics,$x2364-0057 606 $aStatistics 606 $aStatistics and Computing/Statistics Programs$3https://scigraph.springernature.com/ontologies/product-market-codes/S12008 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 606 $aStatistics for Social Sciences, Humanities, Law$3https://scigraph.springernature.com/ontologies/product-market-codes/S17040 615 0$aStatistics. 615 14$aStatistics and Computing/Statistics Programs. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aStatistics for Social Sciences, Humanities, Law. 676 $a519.5 702 $aSakata$b Toshio$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254078403321 996 $aApplied matrix and tensor variate data analysis$91523156 997 $aUNINA