LEADER 01028nam0 22002651i 450 001 UON00409238 005 20231205104733.18 100 $a20120508d1954 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| 1|||| 200 1 $aˆThe ‰history of the Russian hexameter$fby Richard Burgi 210 $aHamden, Connecticut$cThe Shoe String Press$d1954 215 $a208 p.$d21 cm. 606 $aPOESIA RUSSA$3UONC038568$2FI 620 $aUS$dHamden, Connecticut$3UONL004264 676 $a891.7$cLetterature slave orientali. Russo.$v21 700 1$aBURGI$bRichard$3UONV209483$0708690 712 $aThe Shoe String Press$3UONV274277$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00409238 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI SL FL 35 0346 $eSI MR 47919 5 0346 $sBuono 996 $aHistory of the Russian hexameter$91341577 997 $aUNIOR LEADER 03533nam 22005055 450 001 9911020429803321 005 20250808130241.0 010 $a3-031-97973-7 024 7 $a10.1007/978-3-031-97973-6 035 $a(CKB)40161402900041 035 $a(DE-He213)978-3-031-97973-6 035 $a(MiAaPQ)EBC32260898 035 $a(Au-PeEL)EBL32260898 035 $a(NjHacI)9940161402900041 035 $a(EXLCZ)9940161402900041 100 $a20250808d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aData Visualization with Category Theory and Geometry $eWith a Critical Analysis and Refinement of UMAP /$fby Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XIII, 272 p. 91 illus., 36 illus. in color.) 225 1 $aMathematics of Data,$x2731-4111 ;$v3 311 08$a3-031-97972-9 327 $aChapter 1. Introduction -- Chapter 2. Illustrating UMAP on some simple data sets -- Chapter 3. Metrics and Riemannian manifolds -- Chapter 4. Merging fuzzy simplicial sets and metric spaces: A category theoretical approach -- Chapter 5. UMAP -- Chapter 6. IsUMap: An alternative to the UMAP embedding. 330 $aThis open access book provides a robust exposition of the mathematical foundations of data representation, focusing on two essential pillars of dimensionality reduction methods, namely geometry in general and Riemannian geometry in particular, and category theory. Presenting a list of examples consisting of both geometric objects and empirical datasets, this book provides insights into the different effects of dimensionality reduction techniques on data representation and visualization, with the aim of guiding the reader in understanding the expected results specific to each method in such scenarios. As a showcase, the dimensionality reduction method of ?Uniform Manifold Approximation and Projection? (UMAP) has been used in this book, as it is built on theoretical foundations from all the areas we want to highlight here. Thus, this book also aims to systematically present the details of constructing a metric representation of a locally distorted metric space, which is essentially the problem that UMAP is trying to address, from a more general perspective. Explaining how UMAP fits into this broader framework, while critically evaluating the underlying ideas, this book finally introduces an alternative algorithm to UMAP. This algorithm, called IsUMap, retains many of the positive features of UMAP, while improving on some of its drawbacks. 410 0$aMathematics of Data,$x2731-4111 ;$v3 606 $aDimension reduction (Statistics) 615 0$aDimension reduction (Statistics) 676 $a004.0151 700 $aBarth$b Lukas Silvester$01846147 702 $aFahimi$b Hannaneh$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aJoharinad$b Parvaneh$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aJost$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKeck$b Janis$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020429803321 996 $aData Visualization with Category Theory and Geometry$94430247 997 $aUNINA