A generic optimising feature extraction method using multiobjective genetic programming

In this paper, we present a generic, optimising feature extraction method using multiobjective genetic programming. We re-examine the feature extraction problem and show that effective feature extraction can significantly enhance the performance of pattern recognition systems with simple classifiers. A framework is presented to evolve optimised feature extractors that transform an input pattern space into a decision space in which maximal class separability is obtained. We have applied this method to real world datasets from the UCI Machine Learning and StatLog databases to verify our approach and compare our proposed method with other reported results. We conclude that our algorithm is able to produce classifiers of superior (or equivalent) performance to the conventional classifiers examined, suggesting removal of the need to exhaustively evaluate a large family of conventional classifiers on any new problem. (C) 2010 Elsevier B.V. All rights reserved

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Structure and evolution of regular galaxies

https://www.ester.ee/record=b5477396*estTöö on kaitstud 17. märtsil 1972 Tartu Ülikoolis. Originaal vene keeles

OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimisation of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.Comment: Published on Neural Network

An Overview of the Use of Neural Networks for Data Mining Tasks

In the recent years the area of data mining has experienced a considerable demand for technologies that extract knowledge from large and complex data sources. There is a substantial commercial interest as well as research investigations in the area that aim to develop new and improved approaches for extracting information, relationships, and patterns from datasets. Artificial Neural Networks (NN) are popular biologically inspired intelligent methodologies, whose classification, prediction and pattern recognition capabilities have been utilised successfully in many areas, including science, engineering, medicine, business, banking, telecommunication, and many other fields. This paper highlights from a data mining perspective the implementation of NN, using supervised and unsupervised learning, for pattern recognition, classification, prediction and cluster analysis, and focuses the discussion on their usage in bioinformatics and financial data analysis tasks

A further 'degree of freedom' in the rotational evolution of stars

Observational and theoretical investigations provide evidence for non-uniform spot and magnetic flux distributions on rapidly rotating stars, which have a significant impact on their angular momentum loss rate through magnetised winds. Supplementing the formalism of MacGregor & Brenner (1991) with a latitude-dependent magnetised wind model, we analyse the effect of analytically prescribed surface distributions of open magnetic flux with different shapes and degrees of non-uniformity on the rotational evolution of a solar-like star. The angular momentum redistribution inside the star is treated in a qualitative way, assuming an angular momentum transfer between the rigidly-rotating radiative and convective zones on a constant coupling timescale of 15 Myr; for the sake of simplicity we disregard interactions with circumstellar disks. We find that non-uniform flux distributions entail rotational histories which differ significantly from those of classical approaches, with differences cumulating up to 200% during the main sequence phase. Their impact is able to mimic deviations of the dynamo efficiency from linearity of up to 40% and nominal dynamo saturation limits at about 35 times the solar rotation rate. Concentrations of open magnetic flux at high latitudes thus assist in the formation of very rapidly rotating stars in young open clusters, and ease the necessity for a dynamo saturation at small rotation rates. However, since our results show that even minor amounts of open flux at intermediate latitudes, as observed with Zeeman-Doppler imaging techniques, are sufficient to moderate this reduction of the AM loss rate, we suggest that non-uniform flux distributions are a complementary rather than an alternative explanation for very rapid stellar rotation.Comment: 12 pages, 13 figures, accepted for publication by A&

A generalised feedforward neural network architecture and its applications to classification and regression

Shunting inhibition is a powerful computational mechanism that plays an important role in sensory neural information processing systems. It has been extensively used to model some important visual and cognitive functions. It equips neurons with a gain control mechanism that allows them to operate as adaptive non-linear filters. Shunting Inhibitory Artificial Neural Networks (SIANNs) are biologically inspired networks where the basic synaptic computations are based on shunting inhibition. SIANNs were designed to solve difficult machine learning problems by exploiting the inherent non-linearity mediated by shunting inhibition. The aim was to develop powerful, trainable networks, with non-linear decision surfaces, for classification and non-linear regression tasks. This work enhances and extends the original SIANN architecture to a more general form called the Generalised Feedforward Neural Network (GFNN) architecture, which contains as subsets both SIANN and the conventional Multilayer Perceptron (MLP) architectures. The original SIANN structure has the number of shunting neurons in the hidden layers equal to the number of inputs, due to the neuron model that is used having a single direct excitatory input. This was found to be too restrictive, often resulting in inadequately small or inordinately large network structures

Parametrising arbitrary galaxy morphologies: potentials and pitfalls

We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based parametrisation schemes, namely reliability assessment, disentanglement of morphological observables, and PSF modelling. Furthermore, we demonstrate that estimates of the concentration and Sersic index obtained from the Zurich Structure & Morphology catalogue are in excellent agreement with theoretical predictions. We also demonstrate that the incautious use of the concentration index for classification purposes can cause a severe loss of the discriminative information contained in a given data sample. Moreover, we show that, for poorly resolved galaxies, concentration index and M_20 suffer from strong discontinuities, i.e. similar morphologies are not necessarily mapped to neighbouring points in the parameter space. This limits the reliability of these parameters for classification purposes. Two-dimensional Sersic profiles accounting for centroid and ellipticity are identified as the currently most reliable parametrisation scheme in the regime of intermediate signal-to-noise ratios and resolutions, where asymmetries and substructures do not play an important role. We argue that basis functions provide good parametrisation schemes in the regimes of high signal-to-noise ratios and resolutions. Concerning Sersic profiles, we show that scale radii cannot be compared directly for profiles of different Sersic indices. Furthermore, we show that parameter spaces are typically highly nonlinear. This implies that significant caution is required when distance-based classificaton methods are used.Comment: 18 pages, 13 figure