Clustering with neural networks |
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Authors: | Behzad Kamgar-Parsi J. A. Gualtieri J. E. Devaney Behrooz Kamgar-Parsi |
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Affiliation: | (1) Center for Automation Research, University of Maryland, 20742 College Park, MD, USA;(2) NASA Goddard Space Flight Center, Computer Systems Research Facility, Code 635, 20771 Greenbelt, MD, USA;(3) Science Applications Research, 4400 Forbes Boulevard, 20706 Lanham, MD, USA;(4) Centre for Applied Research in Artificial Intelligence, Naval Research Laboratory, 20375 Washington, DC, USA;(5) Present address: Center for Computing and Applied Mathematics, National Institute of Standards and Technology, 20899 Gaithersburg, MD, USA;(6) Present address: Acoustics Division, Naval Research Laboratory, 20375 Washington, DC, USA |
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Abstract: | Partitioning a set ofN patterns in ad-dimensional metric space intoK clusters — in a way that those in a given cluster are more similar to each other than the rest — is a problem of interest in many fields, such as, image analysis, taxonomy, astrophysics, etc. As there are approximatelyKN/K! possible ways of partitioning the patterns amongK clusters, finding the best solution is beyond exhaustive search whenN is large. We show that this problem, in spite of its exponential complexity, can be formulated as an optimization problem for which very good, but not necessarily optimal, solutions can be found by using a Hopfield model of neural networks. To obtain a very good solution, the network must start from many randomly selected initial states. The network is simulated on the MPP, a 128 × 128 SIMD array machine, where we use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also in starting the network from many initial states at once thus obtaining many solutions in one run. We achieve speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of further speedups of three to six orders of magnitude.Supported by a National Research Council-NASA Research Associatship |
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