Publication: Selección diferenciada del conjunto de entrenamiento en redes de neuronas mediante aprendizaje retardado
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2004
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2004-03-10
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Abstract
Las Redes de Neuronas de Base Radial (RNBR) son aproximadores universales, en el sentido de que son capaces de aproximar, con el grado de precisión deseado, cualquier función continua multivariable, siempre que dispongan de un número suficiente de unidades ocultas. Estas redes se caracterizan por poseer características locales, ya que sus neuronas utilizan funciones de activación cuyo valor decrece exponencialmente al alejarse el patrón de entrada de sus centros. Las RNBR son modelos robustos frente a los errores en los datos y su entrenamiento es muy rápido en comparación con otros tipos de redes de neuronas. El principal inconveniente de las RNBR reside en su deficiente capacidad de generalización. Esto se debe a que es necesario un gran número de neuronas ocultas para poder construir una aproximación a la función objetivo mediante la suma de aproximaciones locales, especialmente si la dimensión del espacio de entrada es alta; este elevado número de neuronas ocultas puede influir negativamente en la capacidad de generalización. Se ha comprobado que el nivel de generalización de las redes de neuronas depende significativamente de la calidad de los datos de entrenamiento, y algunos de esos datos pueden ser redundantes o irrelevantes. Con una cuidadosa selección de los patrones de entrenamiento se podría mejorar la capacidad de generalización. Por otra parte, los métodos de aprendizaje retardado o “perezoso” pueden tener una buena capacidad de generalización pues construyen las representaciones de la función objetivo de forma local dependiendo de la nueva muestra de test, pero su precisión en la generalización depende significativa mente del número de patrones que se seleccionen y de la función de distancia utilizada. El objetivo principal de esta tesis consiste en mejorar la capacidad de generalización de las RNBR utilizando un enfoque basado en los métodos de aprendizaje retardado. Para ello, se propone un método de aprendizaje que selecciona automáticamente, del conjunto de entrenamiento, los patrones más apropiados para aproximar cada nueva muestra de test. Este método sigue una estrategia de aprendizaje perezoso, en el sentido de que construye aproximaciones locales centradas alrededor de la nueva muestra. También se pretende que este método sea general, aplicable independientemente del modelo de red de neuronas elegido; de este modo, se podrá aplicar a otros tipos de redes, como el perceptron multicapa. Para evaluar el modelo propuesto, se aplica a diferentes dominios que son representativos de problemas de aproximación de funciones, de predicción de series temporales y de clasificación. Los resultados obtenidos se comparan con los de los métodos de entrenamiento tradicionales, donde se entrenan las RNBR con todas las muestras de entrenamiento disponibles. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Radial Basis Neural Networks (RBNN) are universal approxirnators, in the sense that they are able to approxirnate arbitrarily well any continuous multivariate function, if enough hidden units are provided. These networks have local characteristics, since their neurons use activation functions whose value exponentially decreases when the input pattern moves away from its centers. RNBR are robust modeis and its convergence is very fast compared to other neural models. A poor generalization ability is the main drawback of RNBR. A great number of hidden neurons is necessary to build an approxirnation to the objective function by rneans of the sum of local approxirnations, specially if the dirnension of the input space is high; this high number of hidden neurons can influence negatively to the network performance. It has been shown that the level of generalization of neural networks depends on the quality of the training data, and sorne of those data can be redundant or irrelevant. With a careful selection of the training patterns, better generalization performance rnay be obtained. Qn the other hand, lazy learning rnethods can obtain a good generaliza tion performance because they construct local representations of the objec tive function depending on the new test sample, but its accuracy depends significantly on the number of selected patterns and on the distance function used. The rnain goal of this thesis consists of improving the generalization ability of RNBR using a lazy learning approach. Thus, a learning rnethod that autornatically selects relevant data to answer a particular novel pattern is proposed. This rnethod follows a lazy learning strategy, in the sense that it builds local approxirnations centered around the new sample. Another goal is that the method is applicable independently of the neural rnodel chosen; in this way, it will be possible to apply the rnethod to other types of networks, as rnultilayer perceptron. In order to evaluate the proposed model, it is applied to different domains that are representative of approxirnation function problerns, tirne series pre diction problerns, and classification problerns. Results are cornpared with those of the traditional RBNN training methods, where all the exarnples frorn the training set are used to train the networks.
Radial Basis Neural Networks (RBNN) are universal approxirnators, in the sense that they are able to approxirnate arbitrarily well any continuous multivariate function, if enough hidden units are provided. These networks have local characteristics, since their neurons use activation functions whose value exponentially decreases when the input pattern moves away from its centers. RNBR are robust modeis and its convergence is very fast compared to other neural models. A poor generalization ability is the main drawback of RNBR. A great number of hidden neurons is necessary to build an approxirnation to the objective function by rneans of the sum of local approxirnations, specially if the dirnension of the input space is high; this high number of hidden neurons can influence negatively to the network performance. It has been shown that the level of generalization of neural networks depends on the quality of the training data, and sorne of those data can be redundant or irrelevant. With a careful selection of the training patterns, better generalization performance rnay be obtained. Qn the other hand, lazy learning rnethods can obtain a good generaliza tion performance because they construct local representations of the objec tive function depending on the new test sample, but its accuracy depends significantly on the number of selected patterns and on the distance function used. The rnain goal of this thesis consists of improving the generalization ability of RNBR using a lazy learning approach. Thus, a learning rnethod that autornatically selects relevant data to answer a particular novel pattern is proposed. This rnethod follows a lazy learning strategy, in the sense that it builds local approxirnations centered around the new sample. Another goal is that the method is applicable independently of the neural rnodel chosen; in this way, it will be possible to apply the rnethod to other types of networks, as rnultilayer perceptron. In order to evaluate the proposed model, it is applied to different domains that are representative of approxirnation function problerns, tirne series pre diction problerns, and classification problerns. Results are cornpared with those of the traditional RBNN training methods, where all the exarnples frorn the training set are used to train the networks.
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Keywords
Redes neuronales, Aprendizaje, Inteligencia artificial