O(log₂M) self-organizing map algorithm without learning of neighborhood vectors

In this letter, a new self-organizing map (SOM) algorithm with computational cost O(log₂M) is proposed where M² is the size of a feature map. The first SOM algorithm with O(M²) was originally proposed by Kohonen. The proposed algorithm is composed of the subdividing method and the binary search method. The proposed algorithm does not need the neighborhood functions so that it eliminates the computational cost in learning of neighborhood vectors and the labor of adjusting the parameters of neighborhood functions. The effectiveness of the proposed algorithm was examined by an analysis of codon frequencies of Escherichia coli (E. coli) K12 genes. These drastic computational reduction and accessible application that requires no adjusting of the neighborhood function will be able to contribute to many scientific areas.