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 [...]... 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 Approach to Interpret Internal Representations of Self- Organizing Maps Information-Theoretic... Figures 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. .. Representations of Self- Organizing Maps 15 17 Fig 12 Original data (a), U-matrix (b) and labels (student No.) (c) obtained by the SOM for student survey No 1 Fig 13 Component planes along nine input variables obtained by the the SOM for student survey No .1 then compute the estimated information Figures 16 (a1) and (b1) show final U-matrices for the small and large network, respectively Figures 16 (a2) and (b2)... 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 is maximized (d) Figure 19 (a) shows... 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... 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 variables obtained by the... 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... 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) ... Internal Representations of Self- Organizing Maps Ryotaro Kamimura IT Education Center, 11 17 Kitakaname Hiratsuka Kanagawa 259 -12 92 Japan 1 Introduction In this chapter, we propose a new method to measure the importance of input variables and to examine the effect of the input variables on other components We applied the method to competitive learning, in particular, self- organizing maps, to demonstrate the... Interpret Internal Representations of Self- Organizing Maps Information-Theoretic Approach to Interpret Internal Representations of Self- Organizing Maps 19 21 Fig 17 Original data (a), U-matrix (b) and labels (c) obtained by the SOM for student survey No 2 Fig 18 Component planes obtained by the SOM for student survey No 2 largest for both networks in Figures 21( c1) and (c2) These values are exactly the . 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. Spectral and Spatial Information 299 M. L. Gonçalves, J. A. F. Costa and M. L. A. Netto Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part 4 Chapter 12 Chapter 13 Part 5 Chapter 14 Chapter 15 Chapter