Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Segmenting the market of West Australian senior tourists using an artificial neural network

Measuring perceptions of customers can be a major problem for marketers of tourism and travel services. Much of the problem is to determine which attributes carry most weight in the purchasing decision. Older travellers weigh many travel features before making their travel decisions. This paper presents a descriptive analysis of neural network methodology and provides a research technique that assesses the weighting of different attributes and uses an unsupervised neural network model to describe a consumer-product relationship. The development of this rich class of models was inspired by the neural architecture of the human brain. These models mathematically emulate the neurophysical structure and decision making of the human brain, and, from a statistical perspective, are closely related to generalised linear models. Artificial neural networks or neural networks are, however, nonlinear and do not require the same restrictive assumptions about the relationship between the independent variables and dependent variables. Using neural networks is one way to determine what trade-offs older travellers make as they decide their travel plans. The sample of this study is from a syndicated data source of 200 valid cases from Western Australia. From senior groups, active learner, relaxed family body, careful participants and elementary vacation were identified and discussed. (C) 2003 Published by Elsevier Science Ltd.

Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.

A general-purpose tunable landscape generator

The research literature on metalieuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging real-world optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are made on either the algorithm itself or the problems to which it is applied, or both. As a consequence, metalieuristics are typically evaluated empirically using a set of test problems. Unfortunately, relatively little attention has been given to the development of methodologies and tools for the large-scale empirical evaluation and/or comparison of metaheuristics. In this paper, we propose a landscape (test-problem) generator that can be used to generate optimization problem instances for continuous, bound-constrained optimization problems. The landscape generator is parameterized by a small number of parameters, and the values of these parameters have a direct and intuitive interpretation in terms of the geometric features of the landscapes that they produce. An experimental space is defined over algorithms and problems, via a tuple of parameters for any specified algorithm and problem class (here determined by the landscape generator). An experiment is then clearly specified as a point in this space, in a way that is analogous to other areas of experimental algorithmics, and more generally in experimental design. Experimental results are presented, demonstrating the use of the landscape generator. In particular, we analyze some simple, continuous estimation of distribution algorithms, and gain new insights into the behavior of these algorithms using the landscape generator.

The parameterless self-organizing map algorithm

The parameterless self-organizing map (PLSOM) is a new neural network algorithm based on the self-organizing map (SOM). It eliminates the need for a learning rate and annealing schemes for learning rate and neighborhood size. We discuss the relative performance of the PLSOM and the SOM and demonstrate some tasks in which the SOM fails but the PLSOM performs satisfactory. Finally we discuss some example applications of the PLSOM and present a proof of ordering under certain limited conditions.

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.

A class of self-stabilizing MCA learning algorithms

In this letter, we propose a class of self-stabilizing learning algorithms for minor component analysis (MCA), which includes a few well-known MCA learning algorithms. Self-stabilizing means that the sign of the weight vector length change is independent of the presented input vector. For these algorithms, rigorous global convergence proof is given and the convergence rate is also discussed. By combining the positive properties of these algorithms, a new learning algorithm is proposed which can improve the performance. Simulations are employed to confirm our theoretical results.

IJDWM Special Issue: Advances in Data Mining Applications

This special issue is a collection of the selected papers published on the proceedings of the First International Conference on Advanced Data Mining and Applications (ADMA) held in Wuhan, China in 2005. The articles focus on the innovative applications of data mining approaches to the problems that involve large data sets, incomplete and noise data, or demand optimal solutions.

Statistical racing techniques for improved empirical evaluation of evolutionary algorithms

In empirical studies of Evolutionary Algorithms, it is usually desirable to evaluate and compare algorithms using as many different parameter settings and test problems as possible, in border to have a clear and detailed picture of their performance. Unfortunately, the total number of experiments required may be very large, which often makes such research work computationally prohibitive. In this paper, the application of a statistical method called racing is proposed as a general-purpose tool to reduce the computational requirements of large-scale experimental studies in evolutionary algorithms. Experimental results are presented that show that racing typically requires only a small fraction of the cost of an exhaustive experimental study.

Machine learning for matching astronomy catalogues

An emerging issue in the field of astronomy is the integration, management and utilization of databases from around the world to facilitate scientific discovery. In this paper, we investigate application of the machine learning techniques of support vector machines and neural networks to the problem of amalgamating catalogues of galaxies as objects from two disparate data sources: radio and optical. Formulating this as a classification problem presents several challenges, including dealing with a highly unbalanced data set. Unlike the conventional approach to the problem (which is based on a likelihood ratio) machine learning does not require density estimation and is shown here to provide a significant improvement in performance. We also report some experiments that explore the importance of the radio and optical data features for the matching problem.