Vicens Gaitan

Multidimensional statistical analysis using artificial neural networks: astronomical applications

We present a new method based on artificial neural networks trained with multiseed backpropagation, for displaying an n-dimensional distribution in a projected space of one, two, or three dimensions. As principal component analysis (PCA) the proposed method is useful for extracting information on the structure of the data set, but unlike the PCA the transformation between the original distribution and the projected one is not restricted to be linear. Artificial examples and real astronomical applications are presented in order to show the reliability and potential of the method for the analysis of large astronomical data sets

Use of multilayer feedforward neural nets as a display method for multidimensional distributions.

We present a new method based on multilayer feedforward neural nets for displaying an n-dimensional distribution in a projected space of 1, 2 or 3 dimensions. A fully nonlinear net with several hidden layers is used. Efficient learning is achieved using multi-seed backpropagation. As a principal component analysis (PCA), the proposed method is useful for extracting information on the structure of the data set, but unlike the PCA, the transformation between the original distribution and the projected one is not restricted to be linear. Artificial examples and a real application are presented in order to show the reliability and potential of the method.

USE OF NEURAL NETS TO MEASURE THE τ POLARIZATION AND ITS BAYESIAN INTERPRETATION

We have tested a neural network (NN) technique as a method to determine the helicity of the τ particles in the process: e+e−→(Z0, γ*)→τ+τ−→(ρν)(ρν). It takes into account in a natural way the fact that both taus have different helicity and gives efficiencies comparable to the Bayesian method. We have found this “academic” example a nice way to introduce the analytical interpretation of the net output, showing that these neural nets techniques are equivalent to a Bayesian Decision Rule.

A regularization term to avoid the saturation of the sigmoids in multilayer neural networks.

In this paper we propose a new method to prevent the saturation of any set of hidden units of a multilayer neural network. This method is implemented by adding a regularization term to the standard quadratic error function, which is based on a repulsive action between pairs of patterns.

Test of agreement between two multidimensional empirical distributions

Abstract We present a method to test the agreement between two multidimensional empirical distributions which is not restricted to work with projections in fewer dimensions due to the lack of data, and with the relevant fact that it is free of binning. The method, which can be successfully implemented on layered neural nets, gives a lower bound value on any estimator that measures the inconsistency between the two distributions.

Optimal projection to estimate the proportions of the different subsamples in a given mixture sample

Abstract Given a n -dimensional sample composed of a mixture of m subsamples with different probability density functions (p.d.f.), it is possible to build a ( m − 1)-dimensional distribution that carries all the information about the subsample proportions in the mixture sample. This projection can be estimated without an analytical knowledge of the p.d.f.s of the different subsamples with the aid, for instance, of neural networks. This way, if m − 1 n it is possible to estimate the proportions of the mixture sample in a lower ( m − 1)-dimensional space without losing sensitivity.

Statistical methods in astronomy based on artificial neural network techniques

Abstract Large amounts of astronomical data are becoming common in modern observational projects. Adequate analysis tools need to be developed if one wants to work effectively with the data. In order to extract physical quantities from the data, we have been investigating the application of a computing technique, Artificial Neural Networks (ANNs) to astronomy, and several original methods have resulted. We have developed the following tools: (1) The NNC (Neural Network Classifier, Serra-Ricart et al. 1991, 1994a). We propose a method to classify faint objects from digital astronomical images based on a layered feedforward neural network which has been trained by the backpropagation procedure. (2) The NNA (Neural Network Analysis, Serra-Ricart et al. 1993). We present a new method also based on artificial neural networks techniques, for displaying an n -dimensional distribution in a projected space of 1, 2 or 3 dimensions. As with Principal Component Analysis, the NNA offers powerful ways of extracting information on the data structure and is useful to, a) reduce the number of input variables to its inherent dimensionality (dimension reduction task), and b) identify different groups of objects (clustering task). (3) The NNI (Neural Network Interpolation, Serra-Ricart et al. 1994b). We propose a method for interpolating multidimensional unbinned data, which could also be sparse, using neural networks algorithms.

Hardware Implementation of a Neural Network for High Energy Physics Application

The high speed and parallelism of VLSI Analog Neural Networks make them specially attractive for the treatment of data coming from elementary particle accelerators, which are used in high energy physics. In this paper we show the implementation of an analog neural network with low precision weights, devoted to the reconstitution of tracks: capability of handling 600 pixels/chip at about 2 1012 connections/second, in 40 mm2 (1.5 um ES2) at 100 Mhz.

Use of a Layered Neural Nets as a Display Method for N-Dimensional Disributions

In this paper we present some examples of a method based on layered neural nets, trained with multi-seed backpropagation, to display a n-dimensional distribution in a projected space of 1, 2 or 3 dimensions. The method can be used as encoder.