sentences:  The weighted kernel "k"-means problem further extends this problem by defining a weight formula_21 for each cluster as the reciprocal of the number of elements in the cluster,
  Suppose formula_23 is a matrix of the normalizing coefficients for each point for each cluster formula_24 if formula_25 and zero otherwise.Suppose formula_26 is the kernel matrix for all points.The weighted kernel "k"-means problem with n points and k clusters is given as,
  such that
  such that formula_30.