Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization [Hardcover]

Marc M. Van Hulle (Author)

Book Description

ISBN-10: 0471345075 | ISBN-13: 978-0471345077 | Publication Date: January 21, 2000 | Edition: 1

A new perspective on topographic map formation and the advantages of information-based learning The study of topographic map formation provides us with important tools for both biological modeling and statistical data modeling. Faithful Representations and Topographic Maps offers a unified, systematic survey of this rapidly evolving field, focusing on current knowledge and available techniques for topographic map formation. The author presents a cutting-edge, information-based learning strategy for developing equiprobabilistic topographic maps--that is, maps in which all neurons have an equal probability to be active--clearly demonstrating how this approach yields faithful representations and how it can be successfully applied in such areas as density estimation, regression, clustering, and feature extraction. The book begins with the standard approach of distortion-based learning, discussing the commonly used Self-Organizing Map (SOM) algorithm and other algorithms, and pointing out their inadequacy for developing equiprobabilistic maps. It then examines the advantages of information-based learning techniques, and finally introduces a new algorithm for equiprobabilistic topographic map formation using neurons with kernel-based response characteristics. The complete learning algorithms and simulation details are given throughout, along with comparative performance analysis tables and extensive references. Faithful Representations and Topographic Maps is an excellent, eye-opening guide for neural network researchers, industrial scientists involved in data mining, and anyone interested in self-organization and topographic maps.

Editorial Reviews

From the Back Cover

A new perspective on topographic map formation and the advantages of information-based learning The study of topographic map formation provides us with important tools for both biological modeling and statistical data modeling. Faithful Representations and Topographic Maps offers a unified, systematic survey of this rapidly evolving field, focusing on current knowledge and available techniques for topographic map formation. The author presents a cutting-edge, information-based learning strategy for developing equiprobabilistic topographic maps—that is, maps in which all neurons have an equal probability to be active—clearly demonstrating how this approach yields faithful representations and how it can be successfully applied in such areas as density estimation, regression, clustering, and feature extraction. The book begins with the standard approach of distortion-based learning, discussing the commonly used Self-Organizing Map (SOM) algorithm and other algorithms, and pointing out their inadequacy for developing equiprobabilistic maps. It then examines the advantages of information-based learning techniques, and finally introduces a new algorithm for equiprobabilistic topographic map formation using neurons with kernel-based response characteristics. The complete learning algorithms and simulation details are given throughout, along with comparative performance analysis tables and extensive references. Faithful Representations and Topographic Maps is an excellent, eye-opening guide for neural network researchers, industrial scientists involved in data mining, and anyone interested in self-organization and topographic maps.

About the Author

MARC M. VAN HULLE, PhD, is an associate professor at the K. U. Leuven Medical School in Leuven, Belgium, and a research associate at the Fund for Scientific Research, Flanders, Belgium.

Product Details

• Hardcover: 288 pages
• Publisher: Wiley-Interscience; 1 edition (January 21, 2000)
• Language: English
• ISBN-10: 0471345075
• ISBN-13: 978-0471345077
• Product Dimensions: 9.6 x 6.4 x 0.7 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #4,180,471 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 7 people found the following review helpful:

5.0 out of 5 stars A fresh approach on topographic maps, March 30, 2000

By 

Helge Ritter (Bielefeld, Germany) - See all my reviews

This review is from: Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization (Hardcover)

The book presents a fresh approach on Topographic Maps, emphasizing ``equiprobabilistic'' topographic maps in which all representational units participate with the same probability in the representation. However, the text goes far beyond a monograph on this particular type of topographic maps and provides an excellent exposition of the topic of self-organizing map models in general, discussing their biological motivation and explaining in depth their connections with important statistical concepts such as vector quantization, non-parametric regression and density estimation. The practicioner will find detailed performance comparisons and psoudo code listings that tremendously facilitate an implementation of the described methods. The potential of the newly introduced equiprobabilistic topographic maps is amply demonstrated with detailed treatments of a broad range of application topics. I am convinced that this book marks an important contribution to the field of topographic map representations and that it has the potential to become a major reference for many years.

3 of 3 people found the following review helpful:

5.0 out of 5 stars A New Frontier in Computational Geometry, August 5, 2000

By A Customer

This review is from: Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization (Hardcover)

This is the first monograph devoted to an extremely important aspect of how nature organizes the sensory surfaces in the higher vertebrates. As this work points out, all sensory surfaces in mammals exist as two dimensional maps which project (or map) onto the (folded) two dimensional surface of the cerebral cortex. Previous authors have pointed out that in the case of the visual system, the retinal surface projects onto area V1 in the occipital cortex in a manner which approximates a "quasi-conformal" complex logarithmic function. Other authors have demonstrated that the cochlear basilar membrane also maps onto the auditory cortex in a similar quasi-conformal fashion. And most obviously, the mechano-receptors in our skin map onto the their corresponding cortical sensory areas in a manner which preserves local order of the projection. The important thing to note here is that this mapping of one 2-D surface onto another 2-D surface preserves the local orthogonality of the map coordinates (defn of quasi-conformal). (In the case of the retinal coordinates, they are the simple R, theta coordinates of the visual field and, in the case of the aural (auditory) map, the coordinates appear to be sound intensity (loudness) and frequency (pitch)). Van Hulle (Kohonen, et al.) describes, in vivid detail, how several "self-organizing" algorithms can make this mapping possible. THIS IS THE IMPORTANT POINT CONVEYED IN THIS MAGNIFICENT WORK. "The underlying INFORMATION coordinates of the data being processed by these 2-D onto 2-D mappings is what 'organizes' or defines the form of the mapping." The only point which the author does not address, is the global nature of these mappings. If we consider how the edges of these 2-D maps project onto eachother, there are three possible projections. One forms an ordinary torus and, unfolded looks like the raster scan of a TV set. This mapping is what has been assumed to be what would be followed in the neural projections of the retina onto area V1, but admits an indeterminacy in that there are two "normal" directions to approach the target surface. The second type of projection, when unfolded, resembles a Mobius strip (or Klein bottle for a closed surface). The importance of this type of projection is that there is only one way for neurons to project onto this surface which removes the ambiguity of the first mapping. (This surface is said to be non-orientable and of genus one in topological terms.) If this is in fact how nature chooses to wire the retino-topic projection, then she must also admit one singular point for each "patch" of map. (Consider what happens when you "squish" a Mobius strip made out of a paper strip between two flat surfaces. There is always a "fold".) About seven years ago, when the color distribution in the mammalian visual cortex was illucidated, it was found that the projection areas were made up of a "patch work quilt" of surfaces each with a singular point about which a set of color strips was splayed (like a peacock tail). Perhaps this is the necessary singular point for this type of retinotopic map. I would hope that the author, in his next book (or edition of this book) might address the global issues of these fascinating 2-D onto 2-D mappings, both natural and computational. (Just for closure, the third possible type of 2-D onto 2-D projection forms a hyperbolic surface whose physical significance is far from clear.)

If this review makes any sense to you, Please BUY THIS BOOK! I'm sure that you will be absolutely fascinated by it's content. However, be forwarned, it would be most helpful to have read Kohonen's "Self Organizing Maps", SV, 1995 before diving into this work. It is written in a "bottom up" fashion so a careful review of the Preface and Table of Contents will help in planning a reading strategy.

4.0 out of 5 stars A highly innovative but quite specialized angle!, March 22, 2000

By A Customer

This review is from: Faithful Representations and Topographic Maps: From Distortion- to Information-Based Self-Organization (Hardcover)

For those familiar with the technology and terminology of Kohonen's self-organizing maps, this book is a highly recommendable asset. The insights on the deficiencies of various previously developed techniques and how to improve them are brilliant. Although the matter is presented in a very bottom-up fashion, it is sometimes hard to keep focusing on the big picture while all the different aspects are in-depth explored. This makes the book sometimes hard to understand. Although it was probably never intended to be easily understandable, this is the reason why I didn't give it the full 5 stars.