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

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Improving bankruptcy prediction in micro-entities by using nonlinear effects and non-financial variables

The use of non-parametric methodologies, the introduction of non-financial variables, and the development of models geared towards the homogeneous characteristics of corporate sub-populations have recently experienced a surge of interest in the bankruptcy literature. However, no research on default prediction has yet focused on micro-entities (MEs), despite such firms’ importance in the global economy. This paper builds the first bankruptcy model especially designed for MEs by using a wide set of accounts from 1999 to 2008 and applying artificial neural networks (ANNs). Our findings show that ANNs outperform the traditional logistic regression (LR) models. In addition, we also report that, thanks to the introduction of non-financial predictors related to age, the delay in filing accounts, legal action by creditors to recover unpaid debts, and the ownership features of the company, the improvement with respect to the use of solely financial information is 3.6%, which is even higher than the improvement that involves the use of the best ANN (2.6%)

Training Process Reduction Based On Potential Weights Linear Analysis To Accelarate Back Propagation Network

Learning is the important property of Back Propagation Network (BPN) and finding the suitable weights and thresholds during training in order to improve training time as well as achieve high accuracy. Currently, data pre-processing such as dimension reduction input values and pre-training are the contributing factors in developing efficient techniques for reducing training time with high accuracy and initialization of the weights is the important issue which is random and creates paradox, and leads to low accuracy with high training time. One good data preprocessing technique for accelerating BPN classification is dimension reduction technique but it has problem of missing data. In this paper, we study current pre-training techniques and new preprocessing technique called Potential Weight Linear Analysis (PWLA) which combines normalization, dimension reduction input values and pre-training. In PWLA, the first data preprocessing is performed for generating normalized input values and then applying them by pre-training technique in order to obtain the potential weights. After these phases, dimension of input values matrix will be reduced by using real potential weights. For experiment results XOR problem and three datasets, which are SPECT Heart, SPECTF Heart and Liver disorders (BUPA) will be evaluated. Our results, however, will show that the new technique of PWLA will change BPN to new Supervised Multi Layer Feed Forward Neural Network (SMFFNN) model with high accuracy in one epoch without training cycle. Also PWLA will be able to have power of non linear supervised and unsupervised dimension reduction property for applying by other supervised multi layer feed forward neural network model in future work.Comment: 11 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS 2009, ISSN 1947 5500, Impact factor 0.42

Multilayer optical learning networks

A new approach to learning in a multilayer optical neural network based on holographically interconnected nonlinear devices is presented. The proposed network can learn the interconnections that form a distributed representation of a desired pattern transformation operation. The interconnections are formed in an adaptive and self-aligning fashioias volume holographic gratings in photorefractive crystals. Parallel arrays of globally space-integrated inner products diffracted by the interconnecting hologram illuminate arrays of nonlinear Fabry-Perot etalons for fast thresholding of the transformed patterns. A phase conjugated reference wave interferes with a backward propagating error signal to form holographic interference patterns which are time integrated in the volume of a photorefractive crystal to modify slowly and learn the appropriate self-aligning interconnections. This multilayer system performs an approximate implementation of the backpropagation learning procedure in a massively parallel high-speed nonlinear optical network