Georg Pölzlbauer

Advanced visualization of self-organizing maps with vector fields

Self-Organizing Maps have been applied in various industrial applications and have proven to be a valuable data mining tool. In order to fully benefit from their potential, advanced visualization techniques assist the user in analyzing and interpreting the maps. We propose two new methods for depicting the SOM based on vector fields, namely the Gradient Field and Borderline visualization techniques, to show the clustering structure at various levels of detail. We explain how this method can be used on aggregated parts of the SOM that show which factors contribute to the clustering structure, and show how to use it for finding correlations and dependencies in the underlying data. We provide examples on several artificial and real-world data sets to point out the strengths of our technique, specifically as a means to combine different types of visualizations offering effective multidimensional information visualization of SOMs.

A visualization technique for self-organizing maps with vector fields to obtain the cluster structure at desired levels of detail

Self-organizing maps (SOMs) are a prominent tool for exploratory data analysis. One core task within the utilization of SOMs is the identification of the cluster structure on the map for which several visualization methods have been proposed, yet different application domains may require additional representation of the cluster structure. In this paper, we propose such a method based on pairwise distance calculation. It can be plotted on top of the map lattice with arrows that point to the closest cluster center. A parameter is provided that determines the granularity of the clustering. We provide experimental results and discuss the general applicability of our method, along with a comparison to related techniques.

Decision Manifolds—A Supervised Learning Algorithm Based on Self-Organization

In this paper, we present a neural classifier algorithm that locally approximates the decision surface of labeled data by a patchwork of separating hyperplanes, which are arranged under certain topological constraints similar to those of self-organizing maps (SOMs). We take advantage of the fact that these boundaries can often be represented by linear ones connected by a low-dimensional nonlinear manifold, thus influencing the placement of the separators. The resulting classifier allows for a voting scheme that averages over the classification results of neighboring hyper- planes. Our algorithm is computationally efficient both in terms of training and classification. Further, we present a model selection method to estimate the topology of the classification boundary. We demonstrate the algorithms usefulness on several artificial and real-world data sets and compare it to the state-of-the-art supervised learning algorithms.

The Metro Visualisation of Component Planes for Self-Organising Maps

The self-organising map is a popular unsupervised neural network model which has successfully been used for clustering various kinds of data. To help in understanding the influence of single variables or components on clusterings, we introduce a novel method for the visualisation of component planes for SOMs. The approach presented is based on the discretisation of the components and makes use of the well-known metro map metaphor. It depicts consistent values and their ordering across the map for discretisations of various components and their correlations in terms of directions on the map. In our approach component lines are drawn for each component of the data, allowing the combination of numerous component planes into one plot. We also propose a method to further aggregate these component lines, by grouping highly correlated variables, i.e. similar lines on the map. To show the applicability of our approach we provide experimental results for two popular machine learning data sets.

Investigation of alternative strategies and quality measures for controlling the growth process of the growing hierarchical self-organizing map

The self-organizing map (SOM) is a very popular neural network model for data analysis and visualization of high-dimensional input data. The growing hierarchical self-organizing map (GHSOM) - being one of the many architectures based on the SOM - has the property of dynamically adapting its architecture during training by map growth as well as creating a hierarchical structure of maps, thus reflecting hierarchical relations in the data. This allows for viewing portions of the data at different levels of granularity. We review different SOM quality measures and also investigate alternative strategies as candidates for guiding the growth process of the GHSOM in order to improve the hierarchical representation of the data.

A vector field visualization technique for self-organizing maps

The Self-Organizing Map is one of most prominent tools for the analysis and visualization of high-dimensional data. We propose a novel visualization technique for Self-Organizing Maps which can be displayed either as a vector field where arrows point to cluster centers, or as a plot that stresses cluster borders. A parameter is provided that allows for visualization of the cluster structure at different levels of detail. Furthermore, we present a number of experimental results using standard data mining benchmark data.