Training Radial Basis Neural Networks with the Extended Kalman Filter

Radial basis function (RBF) neural networks provide attractive possibilities for solving signal processing and pattern classification problems. Several algorithms have been proposed for choosing the RBF prototypes and training the network. The selection of the RBF prototypes and the network weights can be viewed as a system identification problem. As such, this paper proposes the use of the extended Kalman filter for the learning procedure. After the user chooses how many prototypes to include in the network, the Kalman filter simultaneously solves for the prototype vectors and the weight matrix. A decoupled extended Kalman filter is then proposed in order to decrease the computational effort of the training algorithm. Simulation results are presented on reformulated radial basis neural networks as applied to the Iris classification problem. It is shown that the use of the Kalman filter results in better learning than conventional RBF networks and faster learning than gradient descent

Evaluation of neural network pattern classifiers for a remote sensing application

This paper evaluates the classification accuracy of three neural network classifiers on a satellite image-based pattern classification problem. The neural network classifiers used include two types of the Multi-Layer-Perceptron (MLP) and the Radial Basis Function Network. A normal (conventional) classifier is used as a benchmark to evaluate the performance of neural network classifiers. The satellite image consists of 2,460 pixels selected from a section (270 x 360) of a Landsat-5 TM scene from the city of Vienna and its northern surroundings. In addition to evaluation of classification accuracy, the neural classifiers are analysed for generalization capability and stability of results. Best overall results (in terms of accuracy and convergence time) are provided by the MLP-1 classifier with weight elimination. It has a small number of parameters and requires no problem-specific system of initial weight values. Its in-sample classification error is 7.87% and its out-of-sample classification error is 10.24% for the problem at hand. Four classes of simulations serve to illustrate the properties of the classifier in general and the stability of the result with respect to control parameters, and on the training time, the gradient descent control term, initial parameter conditions, and different training and testing setshttps://ssrn.com/abstract=1523788%20or%20http://dx.doi.org/10.2139/ssrn.1523788Published versio

A Training Sample Sequence Planning Method for Pattern Recognition Problems

In solving pattern recognition problems, many classification methods, such as the nearest-neighbor (NN) rule, need to determine prototypes from a training set. To improve the performance of these classifiers in finding an efficient set of prototypes, this paper introduces a training sample sequence planning method. In particular, by estimating the relative nearness of the training samples to the decision boundary, the approach proposed here incrementally increases the number of prototypes until the desired classification accuracy has been reached. This approach has been tested with a NN classification method and a neural network training approach. Studies based on both artificial and real data demonstrate that higher classification accuracy can be achieved with fewer prototypes

Evaluation of Neural Pattern Classifiers for a Remote Sensing Application

This paper evaluates the classification accuracy of three neural network classifiers on a satellite image-based pattern classification problem. The neural network classifiers used include two types of the Multi-Layer-Perceptron (MLP) and the Radial Basis Function Network. A normal (conventional) classifier is used as a benchmark to evaluate the performance of neural network classifiers. The satellite image consists of 2,460 pixels selected from a section (270 x 360) of a Landsat-5 TM scene from the city of Vienna and its northern surroundings. In addition to evaluation of classification accuracy, the neural classifiers are analysed for generalization capability and stability of results. Best overall results (in terms of accuracy and convergence time) are provided by the MLP-1 classifier with weight elimination. It has a small number of parameters and requires no problem-specific system of initial weight values. Its in-sample classification error is 7.87% and its out-of-sample classification error is 10.24% for the problem at hand. Four classes of simulations serve to illustrate the properties of the classifier in general and the stability of the result with respect to control parameters, and on the training time, the gradient descent control term, initial parameter conditions, and different training and testing sets. (authors' abstract)Series: Discussion Papers of the Institute for Economic Geography and GIScienc

Diffeomorphic Learning

We introduce in this paper a learning paradigm in which the training data is transformed by a diffeomorphic transformation before prediction. The learning algorithm minimizes a cost function evaluating the prediction error on the training set penalized by the distance between the diffeomorphism and the identity. The approach borrows ideas from shape analysis where diffeomorphisms are estimated for shape and image alignment, and brings them in a previously unexplored setting, estimating, in particular diffeomorphisms in much larger dimensions. After introducing the concept and describing a learning algorithm, we present diverse applications, mostly with synthetic examples, demonstrating the potential of the approach, as well as some insight on how it can be improved