Soft self-organizing map.

Abstract

by John Pui-fai Sum.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 99-104).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Idea of SSOM --- p.3Chapter 1.3 --- Other Approaches --- p.3Chapter 1.4 --- Contribution of the Thesis --- p.4Chapter 1.5 --- Outline of Thesis --- p.5Chapter 2 --- Self-Organizing Map --- p.7Chapter 2.1 --- Introduction --- p.7Chapter 2.2 --- Algorithm of SOM --- p.8Chapter 2.3 --- Illustrative Example --- p.10Chapter 2.4 --- Property of SOM --- p.14Chapter 2.4.1 --- Convergence property --- p.14Chapter 2.4.2 --- Topological Order --- p.15Chapter 2.4.3 --- Objective Function of SOM --- p.15Chapter 2.5 --- Conclusion --- p.17Chapter 3 --- Algorithms for Soft Self-Organizing Map --- p.18Chapter 3.1 --- Competitive Learning and Soft Competitive Learning --- p.19Chapter 3.2 --- How does SOM generate ordered map? --- p.21Chapter 3.3 --- Algorithms of Soft SOM --- p.23Chapter 3.4 --- Simulation Results --- p.25Chapter 3.4.1 --- One dimensional map under uniform distribution --- p.25Chapter 3.4.2 --- One dimensional map under Gaussian distribution --- p.27Chapter 3.4.3 --- Two dimensional map in a unit square --- p.28Chapter 3.5 --- Conclusion --- p.30Chapter 4 --- Application to Uncover Vowel Relationship --- p.31Chapter 4.1 --- Experiment Set Up --- p.32Chapter 4.1.1 --- Network structure --- p.32Chapter 4.1.2 --- Training procedure --- p.32Chapter 4.1.3 --- Relationship Construction Scheme --- p.34Chapter 4.2 --- Results --- p.34Chapter 4.2.1 --- Hidden-unit labeling for SSOM2 --- p.34Chapter 4.2.2 --- Hidden-unit labeling for SOM --- p.35Chapter 4.3 --- Conclusion --- p.37Chapter 5 --- Application to vowel data transmission --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Simulation --- p.45Chapter 5.2.1 --- Setup --- p.45Chapter 5.2.2 --- Noise model and demodulation scheme --- p.46Chapter 5.2.3 --- Performance index --- p.46Chapter 5.2.4 --- Control experiment: random coding scheme --- p.46Chapter 5.3 --- Results --- p.47Chapter 5.3.1 --- Null channel noise (σ = 0) --- p.47Chapter 5.3.2 --- Small channel noise (0 ≤ σ ≤1) --- p.49Chapter 5.3.3 --- Large channel noise (1 ≤σ ≤7) --- p.49Chapter 5.3.4 --- Very large channel noise (σ > 7) --- p.49Chapter 5.4 --- Conclusion --- p.50Chapter 6 --- Convergence Analysis --- p.53Chapter 6.1 --- Kushner and Clark Lemma --- p.53Chapter 6.2 --- Condition for the Convergence of Jou's Algorithm --- p.54Chapter 6.3 --- Alternative Proof on the Convergence of Competitive Learning --- p.56Chapter 6.4 --- Convergence of Soft SOM --- p.58Chapter 6.5 --- Convergence of SOM --- p.60Chapter 7 --- Conclusion --- p.61Chapter 7.1 --- Limitations of SSOM --- p.62Chapter 7.2 --- Further Research --- p.63Chapter A --- Proof of Corollary1 --- p.65Chapter A.l --- Mean Average Update --- p.66Chapter A.2 --- Case 1: Uniform Distribution --- p.68Chapter A.3 --- Case 2: Logconcave Distribution --- p.70Chapter A.4 --- Case 3: Loglinear Distribution --- p.72Chapter B --- Different Senses of neighborhood --- p.79Chapter B.l --- Static neighborhood: Kohonen's sense --- p.79Chapter B.2 --- Dynamic neighborhood --- p.80Chapter B.2.1 --- Mou-Yeung Definition --- p.80Chapter B.2.2 --- Martinetz et al. Definition --- p.81Chapter B.2.3 --- Tsao-Bezdek-Pal Definition --- p.81Chapter B.3 --- Example --- p.82Chapter B.4 --- Discussion --- p.84Chapter C --- Supplementary to Chapter4 --- p.86Chapter D --- Quadrature Amplitude Modulation --- p.92Chapter D.l --- Amplitude Modulation --- p.92Chapter D.2 --- QAM --- p.93Bibliography --- p.9