The graph partitioning problem is a famous combinatorial problem and has many applications including VLSI circuit design, task allocation in distributed computer systems and so on. In this paper, a novel neural network for the m-way graph partitioning problem is proposed where the maximum neuron model is used. The undirected graph with weighted nodes and weighted edges is partitioned into several subsets. The objective of partitioning is to minimize the sum of weights on cut edges with keeping the size of each subset balanced. The proposed algorithm was compared with the genetic algorithm. The experimental result shows that the proposed neural network is better or comparable with the other existing methods for solving the m-way graph partitioning problem in terms of the computation time and the solution quality.

This paper presents a new self-organization classification algorithm for remote-sensing images. Kohonen and other scholars have proposed self-organization algorithms. Kohonen's model easily converges to the local minimum by tuning the elaborate parameters. In addition to others, S. C. Amatur and Y. Takefuji have also proposed self-organization algorithm model. In their algorithm, the maximum neuron model (winner-take-all neuron model) is used where the parameter-tuning is not needed. The algorithm is able to shorten the computation time without a burden on the parameter-tuning. However, their model has a tendency to converge to the local minimum easily. To remove these obstacles produced by the two algorithms, we have proposed a new self-organization algorithm where these two algorithms are fused such that the advantages of the two algorithms are combined. The number of required neurons is the number of pixels multiplied by the number of clusters. The algorithm is composed of two stages: in the first stage we use the maximum self-organization algorithm until the state of the system converges to the local-minimum, then, the Kohonen self-organization algorithm is used in the last stage in order to improve the solution quality by escaping from the local minimum of the first stage. We have simulated a LANDSAT-TM image data with 500 pixel 100 pixel image and 8-bit gray scaled. The results justifies all our claims to the proposed algorithm.