Programme
All talks will be held in lecture hall H6 at the western end of the main hall.
The time for a talk is 20 minutes plus 5 min discussion.
Theory and extensions
Tuesday, 2007-09-04 - from 13:15 to 15:00
Fixed point rules for heteroscedastic Gaussian kernel-based topographic map formation
Presenting Author: Marc M. Van Hulle Authors: Marc M. Van Hulle Abstract:
We develop a number of fixed point rules for training homogeneous, heteroscedastic but otherwise radially-symmetric Gaussian kernel-based topographic maps. We extend the batch map algorithm to the heteroscedastic case and introduce two candidates of fixed point rules for which the end-states, i.e., after the neighborhood range has vanished, are identical to the maximum likelihood Gaussian mixture modeling case. We compare their performance for clustering a number of real world data sets.Emergence in Self Organizing Feature Maps
Presenting Author: Alfred Ultsch Authors: Alfred Ultsch Abstract:
This paper sheds some light on the differences between SOM and emergent SOM (ESOM). The discussion in philosophy and epistemology about Emergence is summarized in the form of postulates. The properties of SOM are compared to these postulates. SOM fulfill most of the postulates. The epistemological postulates regarding this issue are hard, if not impossible, to prove. An alternative postulate relying on semiotic concepts, called "semiotic irreducibility" is proposed here. This concept is applied to U-Matrix on SOM with many neurons. This leads to the definition of ESOM as SOM producing a nontrivial U-Matrix on which the terms "watershed" and "catchment basin" are meaningful and which are cluster conform. The usefulness of the approach is demonstrated with an ESOM clustering algorithm which exploits the emergent properties of such SOM. Results on synthetic data also in blind studies are convincing. The application of ESOM clustering for a real world problem let to an excellent solution.Self-Organizing Homotopy Network
Presenting Author: Tetsuo Furukawa Authors: Tetsuo Furukawa Abstract:
In this paper, we propose a conceptual learning algorithm called the 'self-organizing homotopy (SOH)' together with an implementation thereof. As in the case of the SOM, our SOH organizes a homotopy in a self-organizing manner by giving a set of data episodes. Thus it is an extension of the SOM, moving from a 'map' to a 'homotopy'. From a geometrical viewpoint, the SOH represents a set of (i.e. multiple) data distributions by a fiber bundle, whereas the SOM represents a single data distribution by a manifold. One of the solutions to the SOH is SOM², in which every reference vector unit of the conventional SOM is itself replaced by an SOM. Consequently SOM² has the ability to represent a fiber bundle, i.e. a product manifold, by using a product space of SOM x SOM. It is expected that SOHs will play important roles in the fields of pattern recognition, adaptive functions, context understanding, and others, in which nonlinear manifolds and the homotopy play crucial roles.Indices to Evaluate Self-Organizing Maps for Structures
Presenting Author: J. J. Steil Authors: J. J. Steil, A. Sperduti Abstract:
Self-Organizing Maps for Structures (SOM-SD) are neural networks models capable of processing structured data, such as sequences and trees. The evaluation of the encoding quality achieved by these maps should neither be measured only by the quantization error as in the standard SOM, which fails to capture the structural aspects, nor by other topology preserving indexes which are ill-defined for discrete structures. We propose new indexes for the evaluation of encoding quality which are customized to the structural nature of input data. These indexes are used to evaluate the quality of SOM-SDs trained on a benchmark dataset introduced earlier in. We show that the proposed indexes capture relevant structural features of the tree encoding additional to the statistical features of the training data labels.