LEADER 03448nam  22005775  450 
001 9911031669703321
005 20251001130526.0
010   $a3-031-95785-7
024 7 $a10.1007/978-3-031-95785-7
035   $a(MiAaPQ)EBC32323333
035   $a(Au-PeEL)EBL32323333
035   $a(CKB)41528493200041
035   $a(OCoLC)1543044799
035   $a(DE-He213)978-3-031-95785-7
035   $a(EXLCZ)9941528493200041
100   $a20251001d2025      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLinear Dimensionality Reduction /$fby Alain Franc
205   $a1st ed. 2025.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025.
215   $a1 online resource (281 pages)
225 1 $aLecture Notes in Statistics,$x2197-7186 ;$v228
311 08$a3-031-95784-9 
327   $a- 1. Introduction -- 2. Principal Component Analysis (PCA) -- 3. Complements on PCA -- 4. PCA with Metrics on Rows and Columns -- 5. Correspondence Analysis -- 6. PCA with Instrumental Variables -- 7. Canonical Correlation Analysis -- 8. Multiple Canonical Correlation Analysis -- 9. Multidimensional Scaling.
330   $aThis book provides an overview of some classical linear methods in Multivariate Data Analysis. This is an old domain, well established since the 1960s, and refreshed timely as a key step in statistical learning. It can be presented as part of statistical learning, or as dimensionality reduction with a geometric flavor. Both approaches are tightly linked: it is easier to learn patterns from data in low-dimensional spaces than in high-dimensional ones. It is shown how a diversity of methods and tools boil down to a single core method, PCA with SVD, so that the efforts to optimize codes for analyzing massive data sets like distributed memory and task-based programming, or to improve the efficiency of algorithms like Randomized SVD, can focus on this shared core method, and benefit all methods. This book is aimed at graduate students and researchers working on massive data who have encountered the usefulness of linear dimensionality reduction and are looking for a recipe to implement it. It has been written according to the view that the best guarantee of a proper understanding and use of a method is to study in detail the calculations involved in implementing it. With an emphasis on the numerical processing of massive data, it covers the main methods of dimensionality reduction, from linear algebra foundations to implementing the calculations. The basic requisite elements of linear and multilinear algebra, statistics and random algorithms are presented in the appendix.
410  0$aLecture Notes in Statistics,$x2197-7186 ;$v228
606   $aMultivariate analysis
606   $aBig data
606   $aMachine learning
606   $aMultivariate Analysis
606   $aBig Data
606   $aStatistical Learning
615  0$aMultivariate analysis.
615  0$aBig data.
615  0$aMachine learning.
615 14$aMultivariate Analysis.
615 24$aBig Data.
615 24$aStatistical Learning.
676   $a519.535
700   $aFranc$b Alain$01364666
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9911031669703321
996   $aLinear Dimensionality Reduction$94443083
997   $aUNINA