“Following the very recent line of work on the “generalized min-max” (GMM) kernel, this study proposes the “generalized intersection” (GInt) kernel and the related “normalized generalized min-max” (NGMM) kernel. In computer vision, the (histogram) intersection kernel has been popular, and the GInt kernel generalizes it to data which can have both negative and positive entries. Through an extensive empirical classification study on 40 datasets from the UCI repository, we are able to show that this (tuning-free) GInt kernel performs fairly well.”