A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma

Building Adaptive Basis Functions with a Continuous Self-Organizing Map

This paper introduces CSOM, a continuous version of the Self-Organizing Map (SOM). The CSOM network generates maps similar to those created with the original SOM algorithm but, due to the continuous nature of the mapping, CSOM outperforms the SOM on function approximation tasks. CSOM integrates self-organization and smooth prediction into a single process. This is a departure from previous work that required two training phases, one to self-organize a map using the SOM algorithm, and another to learn a smooth approximation of a function. System performance is illustrated with three examples.Office of Naval Research (N00014-95-10409, N00014-95-0657

Ranked centroid projection: A data visualization approach based on self-organizing maps

The Self-Organizing Map (SOM) is an unsupervised neural network model that provides topology-preserving mapping from high-dimensional input spaces onto a commonly two-dimensional output space. In this study, the clustering and visualization capabilities of the SOM, especially in the analysis of textual data, i.e. document collections, are reviewed and further developed. A novel clustering and visualization approach based on the SOM is proposed for the task of text data mining. The proposed approach first transforms the document space into a multi-dimensional vector space by means of document encoding. Then a growing hierarchical SOM (GHSOM) is trained and used as a baseline framework, which automatically produces maps with various levels of details. Following the training of the GHSOM, a novel projection method, namely the Ranked Centroid Projection (RCP), is applied to project the input vectors onto a hierarchy of two-dimensional output maps. The projection of the input vectors is treated as a vector interpolation into a two-dimensional regular map grid. A ranking scheme is introduced to select the nearest R units around the input vector in the original data space, the positions of which will be taken into account in computing the projection coordinates.The proposed approach can be used both as a data analysis tool and as a direct interface to the data. Its applicability has been demonstrated in this study using an illustrative data set and two real-world document clustering tasks, i.e. the SOM paper collection and the Anthrax paper collection. Based on the proposed approach, a software toolbox is designed for analyzing and visualizing document collections, which provides a user-friendly interface and several exploration and analysis functions.The presented SOM-based approach incorporates several unique features, such as the adaptive structure, the hierarchical training, the automatic parameter adjustment and the incremental clustering. Its advantages include the ability to convey a large amount of information in a limited space with comparatively low computation load, the potential to reveal conceptual relationships among documents, and the facilitation of perceptual inferences on both inter-cluster and within-cluster relationships

Visualization of clusters in geo-referenced data using three-dimensional self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de InformaçãoThe Self-Organizing Map (SOM) is an artificial neural network that performs simultaneously vector quantization and vector projection. Due to this characteristic, the SOM is an effective method for clustering analysis via visualization. The SOM can be visualized through the output space, generally a regular two-dimensional grid of nodes, and through the input space, emphasizing the vector quantization process. Among all the strategies for visualizing the SOM, we are particularly interested in those that allow dealing with spatial dependency, linking the SOM to the geographic visualization with color. One possible approach, commonly used, is the cartographic representation of data with label colors defined from the output space of a two-dimensional SOM. However, in the particular case of geo-referenced data, it is possible to consider the use of a three-dimensional SOM for this purpose, thus adding one more dimension in the analysis. In this dissertation is presented a method for clustering geo-referenced data that integrates the visualization of both perspectives of a three dimensional SOM: linking its output space to the cartographic representation through a ordered set of colors; and exploring the use of frontiers among geo-referenced elements, computed according to the distances in the input space between their Best Matching Units