Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns

This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM) implements SOM-type learning to one-dimensional arrays for individual time units, preserves the orientation with short-term memory and arranges the arrays in an ascending order of time. The two-dimensional representation of the SOTM attempts thus twofold topology preservation, where the horizontal direction preserves time topology and the vertical direction data topology. This enables discovering the occurrence and exploring the properties of temporal structural changes in data. For representing qualities and properties of SOTMs, we adapt measures and visualizations from the standard SOM paradigm, as well as introduce a measure of temporal structural changes. The functioning of the SOTM, and its visualizations and quality and property measures, are illustrated on artificial toy data. The usefulness of the SOTM in a real-world setting is shown on poverty, welfare and development indicators

Hacia el modelado 3d de tumores cerebrales mediante endoneurosonografía y redes neuronales

Las cirugías mínimamente invasivas se han vuelto populares debido a que implican menos riesgos con respecto a las intervenciones tradicionales. En neurocirugía, las tendencias recientes sugieren el uso conjunto de la endoscopia y el ultrasonido, técnica llamada endoneurosonografía (ENS), para la virtualización 3D de las estructuras del cerebro en tiempo real. La información ENS se puede utilizar para generar modelos 3D de los tumores del cerebro durante la cirugía. En este trabajo, presentamos una metodología para el modelado 3D de tumores cerebrales con ENS y redes neuronales. Específicamente, se estudió el uso de mapas auto-organizados (SOM) y de redes neuronales tipo gas (NGN). En comparación con otras técnicas, el modelado 3D usando redes neuronales ofrece ventajas debido a que la morfología del tumor se codifica directamente sobre los pesos sinápticos de la red, no requiere ningún conocimiento a priori y la representación puede ser desarrollada en dos etapas: entrenamiento fuera de línea y adaptación en línea. Se realizan pruebas experimentales con maniquíes médicos de tumores cerebrales. Al final del documento, se presentan los resultados del modelado 3D a partir de una base de datos ENS.Minimally invasive surgeries have become popular because they reduce the typical risks of traditional interventions. In neurosurgery, recent trends suggest the combined use of endoscopy and ultrasound (endoneurosonography or ENS) for 3D virtualization of brain structures in real time. The ENS information can be used to generate 3D models of brain tumors during a surgery. This paper introduces a methodology for 3D modeling of brain tumors using ENS and unsupervised neural networks. The use of self-organizing maps (SOM) and neural gas networks (NGN) is particularly studied. Compared to other techniques, 3D modeling using neural networks offers advantages, since tumor morphology is directly encoded in synaptic weights of the network, no a priori knowledge is required, and the representation can be developed in two stages: off-line training and on-line adaptation. Experimental tests were performed using virtualized phantom brain tumors. At the end of the paper, the results of 3D modeling from an ENS database are presented

How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?

In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel that measures how different or similar two objects are. This approach has been used to define several variants of the Self Organizing Map (SOM). This paper reviews those variants in using a common set of notations in order to outline differences and similarities between them. It discusses the advantages and drawbacks of the variants, as well as the actual relevance of the dissimilarity/kernel SOM for practical applications

Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

Industrial process monitoring by means of recurrent neural networks and Self Organizing Maps

Industrial manufacturing plants often suffer from reliability problems during their day-to-day operations which have the potential for causing a great impact on the effectiveness and performance of the overall process and the sub-processes involved. Time-series forecasting of critical industrial signals presents itself as a way to reduce this impact by extracting knowledge regarding the internal dynamics of the process and advice any process deviations before it affects the productive process. In this paper, a novel industrial condition monitoring approach based on the combination of Self Organizing Maps for operating point codification and Recurrent Neural Networks for critical signal modeling is proposed. The combination of both methods presents a strong synergy, the information of the operating condition given by the interpretation of the maps helps the model to improve generalization, one of the drawbacks of recurrent networks, while assuring high accuracy and precision rates. Finally, the complete methodology, in terms of performance and effectiveness is validated experimentally with real data from a copper rod industrial plant.Postprint (published version

Advances in Self Organising Maps

The Self-Organizing Map (SOM) with its related extensions is the most popular artificial neural algorithm for use in unsupervised learning, clustering, classification and data visualization. Over 5,000 publications have been reported in the open literature, and many commercial projects employ the SOM as a tool for solving hard real-world problems. Each two years, the "Workshop on Self-Organizing Maps" (WSOM) covers the new developments in the field. The WSOM series of conferences was initiated in 1997 by Prof. Teuvo Kohonen, and has been successfully organized in 1997 and 1999 by the Helsinki University of Technology, in 2001 by the University of Lincolnshire and Humberside, and in 2003 by the Kyushu Institute of Technology. The Universit\'{e} Paris I Panth\'{e}on Sorbonne (SAMOS-MATISSE research centre) organized WSOM 2005 in Paris on September 5-8, 2005.Comment: Special Issue of the Neural Networks Journal after WSOM 05 in Pari

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