79 research outputs found
Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner
The magnification behaviour of a generalized family of self-organizing
feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is
analyzed by the magnification law in the one-dimensional case, which can be
obtained analytically. The Winner-Enhancing case allows to acheive a
magnification exponent of one and therefore provides optimal mapping in the
sense of information theory. A numerical verification of the magnification law
is included, and the ordering behaviour is analyzed. Compared to the original
Self-Organizing Map and some other approaches, the generalized Winner Enforcing
Algorithm requires minimal extra computations per learning step and is
conveniently easy to implement.Comment: 6 pages, 5 figures. For an extended version refer to cond-mat/0208414
(Neural Computation 17, 996-1009
Winner-Relaxing Self-Organizing Maps
A new family of self-organizing maps, the Winner-Relaxing Kohonen Algorithm,
is introduced as a generalization of a variant given by Kohonen in 1991. The
magnification behaviour is calculated analytically. For the original variant a
magnification exponent of 4/7 is derived; the generalized version allows to
steer the magnification in the wide range from exponent 1/2 to 1 in the
one-dimensional case, thus provides optimal mapping in the sense of information
theory. The Winner Relaxing Algorithm requires minimal extra computations per
learning step and is conveniently easy to implement.Comment: 14 pages (6 figs included). To appear in Neural Computatio
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
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
Investigation of topographical stability of the concave and convex Self-Organizing Map variant
We investigate, by a systematic numerical study, the parameter dependence of
the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf
concave and convex learning with respect to different input distributions,
input and output dimensions
Magnitude Sensitive Competitive Neural Networks
En esta Tesis se presentan un conjunto de redes neuronales llamadas Magnitude Sensitive Competitive Neural Networks (MSCNNs). Se trata de un conjunto de algoritmos de Competitive Learning que incluyen un tĆ©rmino de magnitud como un factor de modulaciĆ³n de la distancia usada en la competiciĆ³n. Al igual que otros mĆ©todos competitivos, MSCNNs realizan la cuantizaciĆ³n vectorial de los datos, pero el tĆ©rmino de magnitud guĆa el entrenamiento de los centroides de modo que se representan con alto detalle las zonas deseadas, definidas por la magnitud. Estas redes se han comparado con otros algoritmos de cuantizaciĆ³n vectorial en diversos ejemplos de interpolaciĆ³n, reducciĆ³n de color, modelado de superficies, clasificaciĆ³n, y varios ejemplos sencillos de demostraciĆ³n. AdemĆ”s se introduce un nuevo algoritmo de compresiĆ³n de imĆ”genes, MSIC (Magnitude Sensitive Image Compression), que hace uso de los algoritmos mencionados previamente, y que consigue una compresiĆ³n de la imagen variable segĆŗn una magnitud definida por el usuario. Los resultados muestran que las nuevas redes neuronales MSCNNs son mĆ”s versĆ”tiles que otros algoritmos de aprendizaje competitivo, y presentan una clara mejora en cuantizaciĆ³n vectorial sobre ellos cuando el dato estĆ” sopesado por una magnitud que indica el ĀæinterĆ©sĀæ de cada muestra
Financial time series analysis with competitive neural networks
Lāobjectif principal de meĢmoire est la modeĢlisation des donneĢes temporelles non stationnaires. Bien que les modeĢles statistiques classiques tentent de corriger les donneĢes non stationnaires en diffeĢrenciant et en ajustant pour la tendance, je tente de creĢer des grappes localiseĢes de donneĢes de seĢries temporelles stationnaires graĢce aĢ lāalgorithme du Ā« self-organizing map Ā». Bien que de nombreuses techniques aient eĢteĢ deĢveloppeĢes pour les seĢries chronologiques aĢ lāaide du Ā« self- organizing map Ā», je tente de construire un cadre matheĢmatique qui justifie son utilisation dans la preĢvision des seĢries chronologiques financieĢres. De plus, je compare les meĢthodes de preĢvision existantes aĢ lāaide du SOM avec celles pour lesquelles un cadre matheĢmatique a eĢteĢ deĢveloppeĢ et qui nāont pas eĢteĢ appliqueĢes dans un contexte de preĢvision. Je compare ces meĢthodes avec la meĢthode ARIMA bien connue pour la preĢvision des seĢries chronologiques. Le deuxieĢme objectif de meĢmoire est de deĢmontrer la capaciteĢ du Ā« self-organizing map Ā» aĢ regrouper des donneĢes vectorielles, puisquāelle a eĢteĢ deĢveloppeĢe aĢ lāorigine comme un reĢseau neuronal avec lāobjectif de regroupement. Plus preĢciseĢment, je deĢmontrerai ses capaciteĢs de regroupement sur les donneĢes du Ā« limit order book Ā» et preĢsenterai diverses meĢthodes de visualisation de ses sorties.The main objective of this Masterās thesis is in the modelling of non-stationary time series data. While classical statistical models attempt to correct non- stationary data through differencing and de-trending, I attempt to create localized clusters of stationary time series data through the use of the self-organizing map algorithm. While numerous techniques have been developed that model time series using the self-organizing map, I attempt to build a mathematical framework that justifies its use in the forecasting of financial times series. Additionally, I compare existing forecasting methods using the SOM with those for which a framework has been developed and which have not been applied in a forecasting context. I then compare these methods with the well known ARIMA method of time series forecasting. The second objective of this thesis is to demonstrate the self-organizing mapās ability to cluster data vectors as it was originally developed as a neural network approach to clustering. Specifically I will demonstrate its clustering abilities on limit order book data and present various visualization methods of its output
Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 2
Papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake, held 1-3 Jun. 1992 at the Lyndon B. Johnson Space Center in Houston, Texas are included. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making
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