T. Villmann

Topology Preservation in Self-Organizing Maps

Publisher Summary Self-organizing map (SOMs) are special types of neural maps which have found a wide distribution. Neural maps constitute an important neural network paradigm. In brains, neural maps occur in all sensory modalities as well as in motor areas. In technical contexts, neural maps are utilized in the fashion of neighborhood preserving vector quantizers. In both cases, these networks project data from some possibly high-dimensional input space onto a position in some output space. To achieve this projection, neural maps are self-organized by unsupervised learning schemes. It also discusses the problem of topology preservation in self-organizing maps. A mathematically exact definition is developed for this and it show ways of measuring the degree of topology preservation. Finally, advanced learning scheme is also introduced for generating general hypercube structures for self-organizing maps which then yield improved topology preservation for the map.

Association Learning in SOMs for Fuzzy-Classification

We present a general framework for association learning in self-organizing maps (SOMs), which can be specified for the utilization for supervised fuzzy classification. In this way, we obtain a prototype based fuzzy classification model (FLSOM), which can be easily interpreted and visualized due to the fundamental properties of SOMs. Moreover, the provided extension gives the ability to detect class similarities. We apply this approch to classification and class similarity detection for mass spectrometric data in case of cancer disease and obtain comparable results. We demonstrate that the FLSOM-based class similarity detection leads to clinically expected class similarities. Finally, this approach can be taken a semi-supervised learning approach in a twofold sense: association learning is influenced by two terms an unsupervised and a supervised learning term. Further, if no association is given for a data point, only the unsupervised learning amount is applied.

Parallel Evolutionary Algorithms with SOM-Like Migration and their Application to Real World Data Sets

We introduce a multiple subpopulation approach for parallel evolutionary algorithms the migration scheme of which follows a SOM-like dynamics. We succesfully apply this approach to clustering in both VLSI-design and psychotherapy research. The advantages of the approach are shown which consist in a reduced communication overhead between the sub-populations preserving a non-vanishing information flow.

Matrix Metric Adaptation for Improved Linear Discriminant Analysis of Biomedical Data

A structurally simple, yet powerful, formalism is presented for adapting attribute combinations in high-dimensional data, given categorical data class labels. The rank-1 Mahalanobis distance is optimized in a way that maximizes between-class variability while minimizing within-class variability. This optimization target has resemblance to Fishers linear discriminant analysis (LDA), but the proposed formulation is more general and yields improved class separation, which is demonstrated for spectrum data and gene expression data.