Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

A selective learning method to improve the generalization of multilayer feedforward neural networks.

Multilayer feedforward neural networks with backpropagation algorithm have been used successfully in many applications. However, the level of generalization is heavily dependent on the quality of the training data. That is, some of the training patterns can be redundant or irrelevant. It has been shown that with careful dynamic selection of training patterns, better generalization performance may be obtained. Nevertheless, generalization is carried out independently of the novel patterns to be approximated. In this paper, we present a learning method that automatically selects the training patterns more appropriate to the new sample to be predicted. This training method follows a lazy learning strategy, in the sense that it builds approximations centered around the novel sample. The proposed method has been applied to three different domains: two artificial approximation problems and a real time series prediction problem. Results have been compared to standard backpropagation using the complete training data set and the new method shows better generalization abilities.Publicad

Multilayer Kerceptron

Multilayer Perceptrons (MLP) are formulated within Support Vector Machine (SVM) framework by constructing multilayer networks of SVMs. The coupled approximation scheme can take advantage of generalization capabilities of the SVM and the combinatory feature of the hidden layer of MLP. The network, the Multilayer Kerceptron (MLK) assumes its own backpropagation procedure that we shall derive here. Tuning rule will be provided for quadratic cost function, with regularization capability as well. A further appealing property of our approach is that by the aid of the so called kernel trick the MLK computations can be performed in the dual space

Artificial neural networks in geospatial analysis

Artificial neural networks are computational models widely used in geospatial analysis for data classification, change detection, clustering, function approximation, and forecasting or prediction. There are many types of neural networks based on learning paradigm and network architectures. Their use is expected to grow with increasing availability of massive data from remote sensing and mobile platforms