Generalization of the codebook updating method of the k-means algorithm

At each iteration of codebook training, the K-means algorithm finds a new codevector and partition by satisfying the centroid condition and the nearest neighbor condition alternatively and satisfies the iterative descent property. We generalize the codebook updating method of the K-means algorithm without affecting the iterative descent property. We also present and re-interpret several algorithms that are included into the category of the generalized K-means algorithm.