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.

School of Computer Science School of Computer Science Carnegie Mellon University Carnegie Mellon University Pittsburgh, PA 15213 Pittsburgh, PA 15213 Abstract In many vision based tasks, the ability to focus attention on the important portions of a scene is crucial for good performance on the tasks. In this paper we present a simple method of achieving spatial selective attention through the use of a saliency map. The saliency map indicates which regions of the input retina are important for performing the task. The saliency map is created through predictive auto-encoding. The performance of this method is demonstrated on two simple tasks which have multiple very strong distracting features in the input retina. Architectural extensions and application directions for this model are presented. On some tasks this extra input can easily be ignored. Nonetheless, often the similarity between the important input features and the irrelevant features is great enough to interfere with task performance.

We propose an alternative model for mixtures of experts which uses a different parametric form for the gating network. The modified model is trained by the EM algorithm. In comparison with earlier models-trained by either EM or gradient ascent-there is no need to select a learning stepsize. We report simulation experiments which show that the new architecture yields faster convergence. We also apply the new model to two problem domains: piecewise nonlinear function approximation and the combination of multiple previously trained classifiers. 1 INTRODUCTION For the mixtures of experts architecture (Jacobs, Jordan, Nowlan & Hinton, 1991), the EM algorithm decouples the learning process in a manner that fits well with the modular structure and yields a considerably improved rate of convergence (Jordan & Jacobs, 1994).

We first rederive the known results for the'thermodynamic limit' of infinite perceptron size N and show explicitly that 9

We describe an analog VLSI implementation of the ARTI algorithm (Carpenter, 1987).

Casting neural network weights in symbolic terms is crucial for interpreting and explaining the behavior of a network. Additionally, in some domains, a symbolic description may lead to more robust generalization. We present a principled approach to symbolic rule extraction based on the notion of weight templates, parameterized regions of weight space corresponding to specific symbolic expressions. With an appropriate choice of representation, we show how template parameters may be efficiently identified and instantiated to yield the optimal match to a unit's actual weights.

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.

Ni1000 was designed to calculate "city block" distances (Le.

The localization and orientation to various novel or interesting events in the environment is a critical sensorimotor ability in all animals, predator or prey. In mammals, the superior colliculus (SC) plays a major role in this behavior, the deeper layers exhibiting topographically mapped responses to visual, auditory, and somatosensory stimuli. Sensory information arriving from different modalities should then be represented in the same coordinate frame. Auditory cues, in particular, are thought to be computed in head-based coordinates which must then be transformed to retinal coordinates. In this paper, an analog VLSI implementation for auditory localization in the azimuthal plane is described which extends the architecture proposed for the barn owl to a primate eye movement system where further transformation is required. This transformation is intended to model the projection in primates from auditory cortical areas to the deeper layers of the primate superior colliculus. This system is interfaced with an analog VLSI-based saccadic eye movement system also being constructed in our laboratory.

AM techniques were first introduced in soft-competitive learning algorithms[l]. This training procedure was later shown to be closely related to Expectation-Maximization algorithms used by the statistical estimation community[2]. Alternating minimizations search for optimal network weights by breaking the search into two distinct minimization problems. A given network performance functional is extremalized first with respect to one set of network weights and then with respect to the remaining weights. These learning procedures have found applications in the training of local expert systems [3], and in Boltzmann machine training [4]. More recently, convergence rates have been derived by viewing the AM 570 Michael Lemmon.