FU Berlin Digitale Dissertation
Tobias Galliat : Adaptive Multilevel Cluster Analysis by Self-Organizing Box Maps Adaptive Multilevel Cluster Analysis by Self-Organizing Box Maps
|Abstract| |Table of Contents| |More Information|

Abstract The aim of this thesis is a fruitful combination of Perron Cluster analysis and self-organized neural networks within an adaptive multilevel clustering approach that allows a fast and robust identification and an efficient description of clusters in high-dimensional data. In a general variant that needs a correct number of clusters k as an input, this new approach is relevant for a great number of cluster problems since it uses a cluster model that covers geometrically, but also dynamically based clusters. Its essential part is a method called representative clustering that guarantees the applicability to large cluster problems: Based on an adaptive decomposition of the object space via self-organized neural networks, the original problem is reduced to a smaller cluster problem. The general clustering approach can be extended by Perron Cluster analysis so that it can be used for large reversible dynamic cluster problems, even if a correct number of clusters k is unknown a priori. The basic application of the extended clustering approach is the conformational analysis of biomolecules, with great impact in the field of Drug Design. Here, for the first time the analysis of practically relevant and large molecules like an HIV protease inhibitor becomes possible.

Table of Contents Download the whole PhDthesis as a zip-tar file or as zip-File For download in PDF format click the chapter title Title and table of contents 1 Introduction 3 1. Cluster Analysis in High-Dimensional Data 7 1.1 Modeling 8 1.2 Problem reduction via representative clustering 13 1.3 Efficient cluster description 16 1.4 How many clusters? 21 2. Decomposition 23 2.1 General Definition 23 2.2 Approximate box decomposition 25 2.3 Decomposition based representative clustering 27 2.4 Efficient cluster description via approximate box decomposition 34 3. Adaptive Decomposition by Self-Organized Neural Networks 41 3.1 Self-Organizing Maps (SOM) 42 3.2 Self-Organizing Box Maps (SOBM) 44 3.3 Comparison SOM-SOBM 53 3.4 Computational complexity 56 3.5 Practical extensions 57 4. Multilevel Representative Clustering 59 4.1 General approach 59 4.2 Adaptive decomposition refinement 60 4.3 Approach based on Perron Cluster analysis 61 5. Applications 73 5.1 Conformational Analysis of biomolecules 73 5.2 Cluster analysis of insurance customers 87 Conclusion 91 Appendix 93 Symbols 95 Bibliography 97

More Information:
Online available:	http://www.diss.fu-berlin.de/2002/125/indexe.html
Language of PhDThesis:	english
Keywords:	cluster analysis, self-organizing maps, molecular dynamics
DNB-Sachgruppe:	28 Informatik, Datenverarbeitung
Classification MSC:	62H30, 68T05
Date of disputation:	10-Jul-2002
PhDThesis from:	Fachbereich Mathematik u. Informatik, Freie Universität Berlin
First Referee:	Prof. Dr. Dr. h.c. Peter Deuflhard
Second Referee:	Prof. Dr. Peter Rentrop
Contact (Author):	galliat@zib.de
Contact (Advisor):	deuflhard@zib.de
Date created:	18-Jul-2002
Date available:	19-Jul-2002

 

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