A normalization method of input data that conserves the norm information for competitive learning neural network using inner product

Normalization of input vector is essential for a competitive learning neural network using the inner product. In this paper we propose a transformation method of input vector without losing the norm information. To conserve the norm information, an additional vector component concerning the norm is introduced besides the original normalized components of the input vector. By applying the method to Kohonen’s self-organizing feature map, its usefulness is demonstrated. We also propose an optical apparatus for its realization.