A Study of Parallel Self-Organizing Map
  A Parallel Self-Organizing Map (Parallel-SOM) is proposed to modify Kohonen's SOM in parallel computing environment. In this model, two separate layers of neurons are connected together. The number of neurons in both layers and connections between them is the product of the number of all elements of input signals and the number of possible classification of the data. With this structure the conventional repeated learning procedure is modified to learn just once. The once learning manner is more similar to human learning and memorizing activities. During training, weight updating is managed through a sequence of operations among some transformation and operation matrices. Every connection between neurons of input/output layers is considered as a independent processor. In this way, all elements of the Euclidean distance matrix and weight matrix are calculated simultaneously. The minimum distance of every line of distance matrix can be found by Grover's search algorithm. This synchronization feature improves the weight updating sequence significantly. With a typical classification example, the convergence result demonstrates efficient performance of Parallel-SOM. Theoretic analysis and proofs also show some important properties of proposed model. Especially, the paper proves that Parallel-SOM has the same convergence property as Kohonen's SOM, but the complexity of former is reduced obviously. 
Li Weigang (U. of Brasilia)