Principal manifolds for data visualization and dimension reduction
In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA), Multidimensional Scaling (MDS), Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology pre
1 online resource (xxiii, 334 pages) : illustrations (some color)
9783540737506, 9783540737490, 3540737502, 3540737499
213093186
Available in another form:
Front Matter; Developments and Applications of Nonlinear Principal Component Analysis
a Review; Nonlinear Principal Component Analysis: Neural Network Models and Applications; Learning Nonlinear Principal Manifolds by Self-Organising Maps; Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization; Topology-Preserving Mappings for Data Visualisation; The Iterative Extraction Approach to Clustering; Representing Complex Data Using Localized Principal Components with Application to Astronomical Data
English