Principal Manifolds for Data Visualization and Dimension Reduction

Chapter 1 Developments and Applications of Nonlinear Principal Component Analysis – a Review

Chapter 2 Nonlinear Principal Component Analysis: Neural Network Models and Applications

Chapter 3 Learning Nonlinear Principal Manifolds by Self-Organising Maps

Chapter 4 Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization

Chapter 5 Topology-Preserving Mappings for Data Visualisation

Chapter 6 The Iterative Extraction Approach to Clustering

Chapter 7 Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

Chapter 8 Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit

Chapter 9 Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes

Chapter 10 Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms

Chapter 11 On Bounds for Diffusion, Discrepancy and Fill Distance Metrics

Chapter 12 Geometric Optimization Methods for the Analysis of Gene Expression Data

Chapter 13 Dimensionality Reduction and Microarray Data