this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the ill-defined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.

This paper presents a new evolutionary system, i.e., EPNet, for evolving artificial neural networks (ANNs). The evolutionary algorithm used in EPNet is based on Fogel's evolutionary programming (EP) [1], [2], [3]. Unlike most previous studies on evolving ANNs, this paper puts its emphasis on evolving ANN's behaviours. This is one of the primary reasons why EP is adopted. Five mutation operators proposed in EPNet reflect such an emphasis on evolving behaviours. Close behavioural links between parents and their offspring are maintained by various mutations, such as partial training and node splitting. EPNet evolves ANN's architectures and connection weights (including biases 1 ) simultaneously in order to reduce the noise in fitness evaluation. The parsimony of evolved ANNs is encouraged by preferring node/connection deletion to addition. EPNet has been tested on a number of benchmark problems in machine learning and ANNs, such as the parity problem, the medical diagnosis problems (bre...

Model-based clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic model-based clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing model-based clustering algorithms. In this view, clusters are represented as probabilistic models in a model space that is conceptually separate from the data space. For partitional clustering, the view is conceptually similar to the ExpectationMaximization (EM) algorithm. For hierarchical clustering, the graph-based view helps to visualize critical/important distinctions between similarity-based approaches and model-based approaches.

Clustering algorithms aim at modelling fuzzy (i.e., ambiguous) unlabeled patterns efficiently. Our goal is to propose a theoretical framework where clustering systems can be compared on the basis of their learning strategies. In the first part of this work, the following issues are reviewed: relative (probabilistic) and absolute (possibilistic) fuzzy membership functions and their relationships to the Bayes rule, batch and on-line learning, growing and pruning networks, modular network architectures, topologically perfect mapping, ecological nets and neuro-fuzziness. From this discussion an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed as a unifying framework in the comparison of clustering systems. Moreover, a set of functional attributes is selected for use as dictionary entries in our comparison. In the second part of this paper, five clustering algorithms taken from the literature are reviewed and compared on...

This paper presents a new cooperative ensemble learning system (CELS) for designing neural network ensembles. The idea behind CELS is to encourage different individual networks in an ensemble to learn different parts or aspects of a training data so that the ensemble can learn the whole training data better. In CELS, the individual networks are trained simultaneously rather than independently or sequentially. This provides an opportunity for the individual networks to interact with each other and to specialize. CELS can create negatively correlated neural networks using a correlation penalty term in the error function to encourage such specialization. This paper analyzes CELS in terms of bias-variance-covariance tradeoff. CELS has also been tested on the Mackey--Glass time series prediction problem and the Australian credit card assessment problem. The experimental results show that CELS can produce neural network ensembles with good generalization ability.

This paper presents a constructive algorithm for training cooperative neural-network ensembles (CNNEs). CNNE combines ensemble architecture design with cooperative training for individual neural networks (NNs) in ensembles. Unlike most previous studies on training ensembles, CNNE puts emphasis on both accuracy and diversity among individual NNs in an ensemble. In order to maintain accuracy among individual NNs, the number of hidden nodes in individual NNs are also determined by a constructive approach. Incremental training based on negative correlation is used in CNNE to train individual NNs for different numbers of training epochs. The use of negative correlation learning and different training epochs for training individual NNs reflect CNNEs emphasis on diversity among individual NNs in an ensemble. CNNE has been tested extensively on a number of benchmark problems in machine learning and neural networks, including Australian credit card assessment, breast cancer, diabetes, glass, heart disease, letter recognition, soybean, and Mackey--Glass time series prediction problems. The experimental results show that CNNE can produce NN ensembles with good generalization ability.

. A new on-line criterion for identifying "useless" neurons of a self-organizing network is proposed. When this criterion is used in the context of the (formerly developed) growing neural gas model to guide deletions of units, the resulting method is able to closely track nonstationary distributions. Slow changes of the distribution are handled by adaptation of existing units. Rapid changes are handled by removal of "useless" neurons and subsequent insertions of new units in other places. 1 Non-stationary data is difficult to handle : : : Non-stationary data distributions can be found in many technical, biological or economical processes. Self-organizing neural networks have rarely been considered for tracking those distributions since many of the models, e.g. the selforganizing map [6], neural gas [8], or the hypercubical map [1], use decaying adaptation parameters 1 . Once the adaptation strength has decayed, the network is "frozen" and thus unable to react to subsequent changes i...

Prototype based classi cation oers intuitive and sparse models with excellent generalization ability. However, these models usually crucially depend on the underlying Euclidian metric; moreover, online variants likely suer from the problem of local optima. We here propose a generalization of learning vector quantization with three additional features: (I) it directly integrates neighborhood cooperation, hence is less aected by local optima; (II) the method can be combined with any dierentiable similarity measure whereby metric parameters such as relevance factors of the input dimensions can automatically be adapted according to the given data; (III) it obeys a gradient dynamics hence shows very robust behavior, and the chosen objective is related to margin optimization.

A structure composed of local linear perceptrons for approximating global class discriminants is investigated. Such local linear models may be combined in a cooperative or competitive way. In the cooperative model, a weighted sum of the outputs of the local perceptrons is computed where the weight is a function of the distance between the input and the position of the local perceptron. In the competitive model, the cost function dictates a mixture model where only one of the local perceptrons give output. Learning of the local models' positions and the linear mappings they implement are coupled and both supervised. We show that this is preferrable to the uncoupled case where the positions are trained in an unsupervised manner before the separate, supervised training of mappings. We use goodness criteria based on the cross-entropy and give learning equations for both the cooperative and competitive cases. The coupled and uncoupled versions of cooperative and competitive approaches are c...

The ability to grow extra nodes is a potentially useful facility for a self-organising neural network. A network that can add nodes into its map space can approximate the input space more accurately, and often more parsimoniously, than a network with predefined structure and size, such as the Self-Organising Map. In addition, a growing network can deal with dynamic input distributions. Most of the growing networks that have been proposed in the literature add new nodes to support the node that has accumulated the highest error during previous iterations or to support topological structures. This usually means that new nodes are added only when the number of iterations is an integer multiple of some pre-defined constant,