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.

[1]  M. Serra-Ricart,et al.  Multidimensional statistical analysis using artificial neural networks: astronomical applications , 1993 .

[2]  Terence D. Sanger,et al.  Optimal unsupervised learning in a single-layer linear feedforward neural network , 1989, Neural Networks.

[3]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[4]  J. Angel,et al.  Adaptive optics for array telescopes using neural-network techniques , 1990, Nature.

[5]  David Lowe,et al.  The optimised internal representation of multilayer classifier networks performs nonlinear discriminant analysis , 1990, Neural Networks.

[6]  Robert A. Jacobs,et al.  Increased rates of convergence through learning rate adaptation , 1987, Neural Networks.

[7]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[8]  O. Lahav,et al.  Morphological Classification of galaxies by Artificial Neural Networks , 1992 .

[9]  Mark D. Johnston,et al.  Scheduling with neural networks - the case of the hubble space telescope , 1992, Comput. Oper. Res..

[10]  P. GALLINARI,et al.  On the relations between discriminant analysis and multilayer perceptrons , 1991, Neural Networks.

[11]  S. Odewahn,et al.  Automated star/galaxy discrimination with neural networks , 1992 .

[12]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[13]  W. L. Sebok,et al.  Optimal classification of images into stars or galaxies - a Bayesian approach. , 1979 .

[14]  Chris Biemesderfer,et al.  Astronomical Data Analysis Software and Systems X , 2001 .

[15]  Frank Bärmann,et al.  On a class of efficient learning algorithms for neural networks , 1992, Neural Networks.

[16]  Fionn Murtagh,et al.  Multilayer perceptrons for classification and regression , 1991, Neurocomputing.

[17]  Alberto Tesi,et al.  On the Problem of Local Minima in Backpropagation , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  R. Palmer,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[19]  S. Bowyer,et al.  Parameter estimation in X-ray astronomy , 1976 .

[20]  Thomas P. Vogl,et al.  Rescaling of variables in back propagation learning , 1991, Neural Networks.

[21]  Eric Saund,et al.  Dimensionality-Reduction Using Connectionist Networks , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Lluís Garrido,et al.  Use of Neural Nets to Measure The? Polarization and its Bayesian Interpretation , 1991, Int. J. Neural Syst..

[23]  Y. Avni,et al.  Energy spectra of X-ray clusters of galaxies , 1976 .

[24]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.