An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebb-like learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this model has no parameters which change over time and is able to continue learning, adding units and connections, until a performance criterion has been met. Applications of the model include vector quantization, clustering, and interpolation.

Understanding knowledge representations in neural nets has been a difficult problem. Principal components analysis (PCA) of contributions (products of sending activations and connection weights) has yielded valuable insights into knowledge representations, but much of this work has focused on the correlation matrix of contributions. The present work shows that analyzing the variance-covariance matrix of contributions yields more valid insights by taking account of weights.

K-Means is a popular clustering algorithm used in many applications, including the initialization of more computationally expensive algorithms (Gaussian mixtures, Radial Basis Functions, Learning Vector Quantization and some Hidden Markov Models). The practice of this initialization procedure often gives the frustrating feeling that K-Means performs most of the task in a small fraction of the overall time. This motivated us to better understand this convergence speed. A second reason lies in the traditional debate between hard threshold (e.g.

A self-organizing neural network for sequence classification called SARDNET is described and analyzed experimentally. SARDNET extends the Kohonen Feature Map architecture with activation retention and decay in order to create unique distributed response patterns for different sequences.

This paper studies the problem of diffusion in Markovian models, such as hidden Markov models (HMMs) and how it makes very difficult the task of learning of long-term dependencies in sequences. Using results from Markov chain theory, we show that the problem of diffusion is reduced if the transition probabilities approach 0 or 1. Under this condition, standard HMMs have very limited modeling capabilities, but input/output HMMs can still perform interesting computations.

We present a new algorithm for finding low complexity networks with high generalization capability. The algorithm searches for large connected regions of so-called ''fiat'' minima of the error function. In the weight-space environment of a "flat" minimum, the error remains approximately constant. Using an MDL-based argument, flat minima can be shown to correspond to low expected overfitting. Although our algorithm requires the computation of second order derivatives, it has backprop's order of complexity. Experiments with feedforward and recurrent nets are described. In an application to stock market prediction, the method outperforms conventional backprop, weight decay, and "optimal brain surgeon".

Networks of this type have a single layer of units with a selective response for some range of the input variables. Earn unit has an overall response function, possibly a Gaussian: D_("')

In this paper we consider the capacity of a binary associative net (Willshaw, Buneman, & Longuet-Higgins, 1969; Willshaw, 1971; Buckingham, 1991) containing these features. While the associative net is a very simple model of associative memory, its behaviour as a storage device is not trivial and yet it is tractable to theoretical analysis.

Although artificial neural networks have been applied in a variety of real-world scenarios with remarkable success, they have often been criticized for exhibiting a low degree of human comprehensibility. Techniques that compile compact sets of symbolic rules out of artificial neural networks offer a promising perspective to overcome this obvious deficiency of neural network representations. This paper presents an approach to the extraction of if-then rules from artificial neural networks. Its key mechanism is validity interval analysis, which is a generic tool for extracting symbolic knowledge by propagating rule-like knowledge through Backpropagation-style neural networks. Empirical studies in a robot arm domain illustrate the appropriateness of the proposed method for extracting rules from networks with real-valued and distributed representations.

Dynamic Cell Structures (DCS) represent a family of artificial neural architectures suited both for unsupervised and supervised learning. They belong to the recently [Martinetz94] introduced class of Topology Representing Networks (TRN) which build perlectly topology preserving feature maps. DCS empI'oy a modified Kohonen learning rule in conjunction with competitive Hebbian learning. The Kohonen type learning rule serves to adjust the synaptic weight vectors while Hebbian learning establishes a dynamic lateral connection structure between the units reflecting the topology of the feature manifold. In case of supervised learning, i.e. function approximation, each neural unit implements a Radial Basis Function, and an additional layer of linear output units adjusts according to a delta-rule. DCS is the first RBF-based approximation scheme attempting to concurrently learn and utilize a perfectly topology preserving map for improved performance. Simulations on a selection of CMU-Benchmarks indicate that the DCS idea applied to the Growing Cell Structure algorithm [Fritzke93] leads to an efficient and elegant algorithm that can beat conventional models on similar tasks.