Clustering is importa nt in m any fields including m anufactlll'ing,

Calculation of Q(t) and R(t) using (4, 5, 7, 9) to execute the path average and the average over sets is relatively straightforward, albeit tedious. We find that -"Yt(l -"Yt)

However, because of the separation between excitation and inhibition, biological neural networks are asymmetrical. We study characteristic differences between asymmetrical networks and their symmetrical counterparts, showing that they have dramatically different dynamical behavior and also how the differences can be exploited for computational ends. We illustrate our results in the case of a network that is a selective amplifier.

This paper presents a novel and fast k-NN classifier that is based on a binary CMM (Correlation Matrix Memory) neural network. A robust encoding method is developed to meet CMM input requirements. A hardware implementation of the CMM is described, which gives over 200 times the speed of a current mid-range workstation, and is scaleable to very large problems. When tested on several benchmarks and compared with a simple k-NN method, the CMM classifier gave less than I % lower accuracy and over 4 and 12 times speedup in software and hardware respectively.

We compute upper and lower bounds on the VC dimension of feedforward networks of units with piecewise polynomial activation functions. We show that if the number of layers is fixed, then the VC dimension grows as W log W, where W is the number of parameters in the network. The VC dimension is an important measure of the complexity of a class of binaryvalued functions, since it characterizes the amount of data required for learning in the PAC setting (see [BEHW89, Vap82]). In this paper, we establish upper and lower bounds on the VC dimension of a specific class of multi-layered feedforward neural networks. Let F be the class of binary-valued functions computed by a feed forward neural network with W weights and k computational (non-input) units, each with a piecewise polynomial activation function.

Visual input liB persists after onset, and initializes the activity levels 9x (XiO). The activities are then modified by the contextual influences. Depending on the visual input, the system often settles into an oscillatory state (Gray A VI Modelo/Pop Out and Asymmetry in Visual Search 799 and Singer, 1989, see the details in Li 1998b). Temporal averages of gx(XiO) over several oscillation cycles are used as the model's output. The nature of the computation performed by the model is determined largely by the horizontal connections J and W, which are local (spanning only a few hypercolumns), and translation and rotation invariant (Figure 1B).

We have proved that the model learned by BLHT converges to the optimal model in given hypothesis space, 1{, which provides the most accurate predictions of percepts and rewards, given short-term memory. We believe this fact provides a solid basis for BLHT, and BLHT can be compared favorably with other methods using short-term memory.

We present a new energy-minimization framework for the graph isomorphism problem which is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. To solve the program we use "replicator" equations, a class of simple continuous-and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inability to escape from local solutions, they nevertheless provide experimental results which are competitive with those obtained using more elaborate mean-field annealing heuristics. 1 INTRODUCTION The graph isomorphism problem is one of those few combinatorial optimization problems which still resist any computational complexity characterization [6]. Despite decades of active research, no polynomial-time algorithm for it has yet been found.

Cluster analysis is a fundamental principle in exploratory data analysis, providing the user with a description of the group structure of given data. A key problem in this context is the interpretation and visualization of clustering solutions in high-dimensional or abstract data spaces. In particular, probabilistic descriptions of the group structure, essential to capture inter-cluster relationships, are hardly assessable by simple inspection ofthe probabilistic assignment variables. VVe present a novel approach to the visualization of group structure. It is based on a statistical model of the object assignments which have been observed or estimated by a probabilistic clustering procedure. The objects or data points are embedded in a low dimensional Euclidean space by approximating the observed data statistics with a Gaussian mixture model. The algorithm provides a new approach to the visualization of the inherent structure for a broad variety of data types, e.g.

Learning Real-Time A* (LRTA*) is a popular control method that interleaves planning and plan execution and has been shown to solve search problems in known environments efficiently. In this paper, we apply LRTA * to the problem of getting to a given goal location in an initially unknown environment. Uninformed LRTA * with maximal lookahead always moves on a shortest path to the closest unvisited state, that is, to the closest potential goal state. This was believed to be a good exploration heuristic, but we show that it does not minimize the worst-case plan-execution time compared to other uninformed exploration methods. This result is also of interest to reinforcement-learning researchers since many reinforcement learning methods use asynchronous dynamic programming, interleave planning and plan execution, and exhibit optimism in the face of uncertainty, just like LRTA *.