3 research outputs found
Beta Scale Invariant Map
In this study we present a novel version of the Scale Invariant Map (SIM) called Beta-SIM, developed to facilitate the clustering and visualization of the internal structure of complex datasets effectively and efficiently. It is based on the application of a family of learning rules derived from the Probability Density Function (PDF) of the residual based on the beta distribution, when applied to the Scale Invariant Map. The Beta-SIM behavior is thoroughly analyzed and successfully demonstrated over 2 artificial and 16 real datasets, comparing its results, in terms of three performance quality measures with other well-known topology preserving models such as Self Organizing Maps (SOM), Scale Invariant Map (SIM), Maximum Likelihood Hebbian Learning-SIM (MLHL-SIM), Visualization Induced SOM (ViSOM), and Growing Neural Gas (GNG). Promising results were found for Beta-SIM, particularly when dealing with highly complex datasets
Beta hebbian learning: definition and analysis of a new family of learning rules for exploratory projection pursuit
[EN] This thesis comprises an investigation into the derivation of learning rules in artificial neural networks from probabilistic criteria.
•Beta Hebbian Learning (BHL).
First of all, it is derived a new family of learning rules which are based on maximising the likelihood of the residual from a negative feedback network when such residual is deemed to come from the Beta Distribution, obtaining an algorithm called Beta Hebbian Learning, which outperforms current neural algorithms in Exploratory Projection Pursuit.
• Beta-Scale Invariant Map (Beta-SIM).
Secondly, Beta Hebbian Learning is applied to a well-known Topology Preserving Map algorithm called Scale Invariant Map (SIM) to design a new of its version called Beta-Scale Invariant Map (Beta-SIM). It is developed to facilitate the clustering and visualization of the internal structure of high dimensional complex datasets effectively and efficiently, specially those characterized by having internal radial distribution. The Beta-SIM behaviour is thoroughly analysed comparing its results, in terms performance quality measures with other well-known topology preserving models.
• Weighted Voting Superposition Beta-Scale Invariant Map (WeVoS-Beta-SIM).
Finally, the use of ensembles such as the Weighted Voting Superposition (WeVoS) is tested over the previous novel Beta-SIM algorithm, in order to improve its stability and to generate accurate topology maps when using complex datasets. Therefore, the WeVoS-Beta-Scale Invariant Map (WeVoS-Beta-SIM), is presented, analysed and compared with other well-known topology preserving models.
All algorithms have been successfully tested using different artificial datasets to corroborate their properties and also with high-complex real datasets.[ES] Esta tesis abarca la investigación sobre la derivación de reglas de aprendizaje en redes neuronales
artificiales a partir de criterios probabilÃsticos.
• Beta Hebbian Learning (BHL).
En primer lugar, se deriva una nueva familia de reglas de aprendizaje basadas en maximizar la
probabilidad del residuo de una red con retroalimentación negativa cuando se considera que
dicho residuo proviene de la Distribución Beta, obteniendo un algoritmo llamado Beta Hebbian
Learning, que mejora a algoritmos neuronales actuales de búsqueda de proyecciones
exploratorias.
• Beta-Scale Invariant Map (Beta-SIM).
En Segundo lugar, Beta Hebbian Learning se aplica a un conocido algoritmo de Mapa de
Preservación de la TopologÃa llamado Scale Invariant Map (SIM) para diseñar una nueva versión
llamada Beta-Scale Invariant Map (Beta-SIM). Este nuevo algoritmo ha sido desarrollado para
facilitar el agrupamiento y visualización de la estructura interna de conjuntos de datos complejos
de alta dimensionalidad de manera eficaz y eficiente, especialmente aquellos caracterizados por
tener una distribución radial interna. El comportamiento de Beta-SIM es analizado en
profundidad comparando sus resultados, en términos de medidas de calidad de rendimiento con
otros modelos bien conocidos de preservación de topologÃa.
• Weighted Voting Superposition Beta-Scale Invariant Map (WeVoS-Beta-SIM).
Finalmente, el uso de ensembles como el Weighted Voting Superposition (WeVoS) sobre el
algoritmo Beta-SIM es probado, con objeto de mejorar su estabilidad y generar mapas
topológicos precisos cuando se utilizan conjuntos de datos complejos. Por lo tanto, se presenta,
analiza y compara el WeVoS-Beta-Scale Invariant Map (WeVoS-Beta-SIM) con otros modelos
bien conocidos de preservación de topologÃa.
Todos los algoritmos han sido probados con éxito sobre conjuntos de datos artificiales para corroborar
sus propiedades, asà como con conjuntos de datos reales de gran complejidad