SELF ORGANIZING MAPS APPLICATIONS AND NOVEL ALGORITHM DESIGN pot

SELF ORGANIZING MAPS ͳ APPLICATIONS AND NOVEL ALGORITHM DESIGN Edited by Josphat Igadwa Mwasiagi Self Organizing Maps - Applications and Novel Algorithm Design Edited by Josphat Igadwa Mwasiagi Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Jelena Marusic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright riri, 2010. Used under license from Shutterstock.com First published January, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Self Organizing Maps - Applications and Novel Algorithm Design, Edited by Josphat Igadwa Mwasiagi p. cm. ISBN 978-953-307-546-4 free online editions of InTech Books and Journals can be found at www.intechopen.com [...]... 21(a2) and (b2), and the importance of input variable No 4 is the 18 20 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 16 U-matrices (1), the ratio RE (2), the values of importance (3) and the probability p( j) (4) for the small-sized (a) and large-sized network (b) Information-Theoretic Approach to Interpret Internal Representations of Self- Organizing. .. in competitive learning 6 8 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design ε ε ε Fig 4 Importance p(k) with large (a), small and estimated importance (c) Fig 5 Importance p(k) with large (a), small and estimated importance (c) Information-Theoretic Approach to Interpret Internal Representations of Self- Organizing Maps Information-Theoretic Approach... four different values of the parameter (a)-(d) and the estimated p( j) with the optimal values of two parameters (e), (f) 13 15 14 16 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 11 U-matrices (1), the ratio RE (2), the values of importance (3) and probabilities p( j) for the small-sized (a) and large-sized network (b) Information-Theoretic... also conducted by Kenta Aoyama, December 2009 16 18 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 14 Information as a function of the parameter σ (a) and the parameter (b); optimal values of the parameter σ as a function of the parameter (c); the ratio RE as a function of the parameter ; and competitive unit output p( j) when the information... between competitive units and input patterns, represents competitive processes (Kamimura & Kamimura, 2000; Kamimura et al., 2001; Kamimura, 2003a;b;c;d) Thus, this information, or more exactly, mutual information, should be as large as possible On the other hand, we can consider 4 6 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 2 Competitive... figure, the information is increased to a maximum point when the parameter is increased to 0.3, and 4 http://www1.ics.uci.edu/ mlearn/MLRepository.html 20 22 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 19 Information as a function of the parameter σ (a) and the parameter (b) Optimal values of the parameter σ as a function of the parameter (c)... middle of the map can be seen, while for the small size, a clear boundary can be generated 22 24 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design Fig 21 U-matrices (1), the ratio RE (2), the values of importance (3) and p( j) (4) for the small-sized (a) and large-sized network (b) ... variables In addition, we plot the estimated firing probability p( j) with the optimal values of the parameters in Figure 10(e) and (f) As the probability p( j) increases, the corresponding 12 14 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design competitive unit responds to the larger number of input patterns As can be seen in the figure, the higher values of... variables (attributes) for measuring the importance of input variables In addition, 2 4 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design (Garcez et al., 2001) pointed out that the pruning of input vectors maintained the highest possible precision On the other hand, in machine learning, variable selection or the interpretation of input variables has... middle of the U-matrix, clear boundaries in warmer colors can be 1 We will discuss this problem in the discussion section 10 12 Self Applications and Novel Achievements Self Organizing Maps - Organising Maps, NewAlgorithm Design s Fig 7 Original data xk (a), U-matrix (b) and labels (c) for the symmetric data obtained by the SOM (1) (2) (3) (4) (5) (6) (7) (8) Fig 8 Component planes along eight input . SELF ORGANIZING MAPS ͳ APPLICATIONS AND NOVEL ALGORITHM DESIGN Edited by Josphat Igadwa Mwasiagi Self Organizing Maps - Applications and Novel Algorithm Design Edited by Josphat. the self- organizing map is also an attempt to 4 Self Organizing Maps - Applications and Novel Algorithm Design Information-Theoretic Approach to Interpret Internal Representations of Self- Organizing. (a) and mutual information maximization (b). The black and white competitive units represent the strong and weak firing rates, respectively. 6 Self Organizing Maps - Applications and Novel Algorithm