  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.
  The empirical results also demonstrate that the NGMM kernel typically
outperforms the GInt kernel. Interestingly, the NGMM kernel has another
interpretation --- it is the ``asymmetrically transformed'' version of the GInt
kernel, based on the idea of ``asymmetric hashing''. Just like the GMM kernel,
the NGMM kernel can be efficiently linearized through (e.g.,) generalized
consistent weighted sampling (GCWS), as empirically validated in our study.
Owing to the discrete nature of hashed values, it also provides a scheme for
approximate near neighbor search.
