  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.
