Massively Parallel Cellular Matrix Model for Self-organizing Map Applications

We propose the concept of parallel cellular matrix which partitions the Euclidean plane defined by input data into an appropriate number of uniform cell units. Each cell is responsible of a certain part of the data and the network of the self-organizing map (SOM), and carries out massive parallel spiral searches based on the cellular matrix topology. The advantage of the proposed model is that it is decentralized and based on data decomposition. The required processing units and memory are with linearly increasing relationship to the problem size. Based on the cellular matrix model, the parallel SOM is implemented to deal with various applications including the traveling salesman problem, structured mesh generation, and superpixel adaptive segmentation map. Experimental results of our GPU implementation show that the running time increases in a linear way with a very weak increasing coefficient according to the input size. The proposed cellular matrix model is suitable to deal with large scale problems in a massively parallel way.