Generalized Intersection Kernel

TL;DR

This paper introduces the generalized intersection (GInt) kernel and the normalized GMM (NGMM) kernel, extending histogram intersection to data with negative entries, and demonstrates their effectiveness in classification tasks with efficient linearization and approximate nearest neighbor search.

Contribution

It proposes the GInt and NGMM kernels, extending existing kernels to handle negative data and providing efficient linearization and hashing methods for practical applications.

Findings

GInt kernel performs well across 40 datasets.

NGMM kernel generally outperforms GInt.

NGMM enables efficient hashing for near neighbor search.

Abstract

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.