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 approximatelyK N/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.

It is shown that the problem of partitioning a net of N patterns in a d-dimensional metric space into K clusters can, in spite of its exponential complexity, be formulated as an optimization problem for which very good, but not necessary optimal, solutions can be found by using a neural network. The network starts from many randomly selected initial states. The network is simulated on the MPP (a 128*128 SIMD array machine), where the massive parallelism is used not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Speedups of two to three orders of magnitude over serial implementations are obtained. Through analog VLSI implementations, speedups commensurate with human perceptual abilities should be possible.<>