Data clustering amounts to a combinatorial optimization problem to re(cid:173) duce the complexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum en(cid:173) tropy framework. For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal num(cid:173) ber of clusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space.

The dynamics of complex neural networks modelling the self(cid:173) organization process in cortical maps must include the aspects of long and short-term memory. The behaviour of the network is such characterized by an equation of neural activity as a fast phenom(cid:173) enon and an equation of synaptic modification as a slow part of the neural system. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables. We also show the consequences of the stability analysis on the neural net parameters.

The dynamics of complex neural networks modelling the selforganization process in cortical maps must include the aspects of long and short-term memory. The behaviour of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables. We also show the consequences of the stability analysis on the neural net parameters. 1 INTRODUCTION This paper investigates a special class of laterally inhibited neural networks. In particular, we have examined the dynamics of a restricted class of laterally inhibited neural networks from a rigorous analytic standpoint.

The dynamics of complex neural networks modelling the selforganization process in cortical maps must include the aspects of long and short-term memory. The behaviour of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables. We also show the consequences of the stability analysis on the neural net parameters. 1 INTRODUCTION This paper investigates a special class of laterally inhibited neural networks. In particular, we have examined the dynamics of a restricted class of laterally inhibited neural networks from a rigorous analytic standpoint.

Anke Meyer-Base Institute of Technical Informatics Technical University of Darmstadt Darmstadt, Germany 64283 Abstract The dynamics of complex neural networks modelling the selforganization processin cortical maps must include the aspects of long and short-term memory. The behaviour of the network is such characterized by an equation of neural activity as a fast phenomenon andan equation of synaptic modification as a slow part of the neural system. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables. We also show the consequences of the stability analysis on the neural net parameters. 1 INTRODUCTION This paper investigates a special class of laterally inhibited neural networks. In particular, we have examined the dynamics of a restricted class of laterally inhibited neural networks from a rigorous analytic standpoint.

Data clustering amounts to a combinatorial optimization problem to reduce the complexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework. For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number of clusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss an objective function for the joint optimization of distortion errors and the complexity of a reduced data representation. A maximum entropy estimation of the cluster assignments yields a unifying framework for clustering algorithms with a number of different distortion and complexity measures. The close analogy of complexity optimized clustering with winner-take-all neural networks suggests a neural-like implementation resembling topological feature maps (see Figure 1).

Data clustering amounts to a combinatorial optimization problem to reduce the complexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework. For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number of clusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss an objective function for the joint optimization of distortion errors and the complexity of a reduced data representation. A maximum entropy estimation of the cluster assignments yields a unifying framework for clustering algorithms with a number of different distortion and complexity measures. The close analogy of complexity optimized clustering with winner-take-all neural networks suggests a neural-like implementation resembling topological feature maps (see Figure 1).

Data clustering amounts to a combinatorial optimization problem to reduce thecomplexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework.For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number ofclusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss anobjective function for the joint optimization of distortion errors and the complexity of a reduced data representation.