Principal Manifolds for Data Visualization and Dimension Reduction

• Corporate Author: SpringerLink (Online service)
• Other Authors: Gorban, Alexander N. (Editor), Kégl, Balázs (Editor), Wunsch, Donald C. (Editor), Zinovyev, Andrei Y. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Computational Science and Enginee, 58
• Subjects: Engineering.; Science.; Computer mathematics.; Physics.; Statistics.; Computational intelligence.; Control engineering.; Control.; Science, general.; Computational Science and Engineering.; Mathematical Methods in Physics.; Computational Intelligence.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.

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 (SO...

Table of Contents:

• 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
• Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit
• Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
• Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
• On Bounds for Diffusion, Discrepancy and Fill Distance Metrics
• Geometric Optimization Methods for the Analysis of Gene Expression Data
• Dimensionality Reduction and Microarray Data
• PCA and K-Means Decipher Genome.