Multiresolution Kernels

TL;DR

This paper introduces a multiresolution kernel methodology that leverages nested component decompositions of structured data, enabling detailed local and global similarity comparisons, with promising results in image retrieval.

Contribution

The paper proposes a novel multiresolution kernel framework that utilizes nested decompositions of data objects, enhancing similarity measures for structured data types.

Findings

Effective in image retrieval tasks

Balances local and global similarity measures

Utilizes a factorization trick for computational efficiency

Abstract

We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures and takes advantage of a more detailed "bag of components" representation of the objects. To obtain such a detailed description, we consider possible decompositions of the original bag into a collection of nested bags, following a prior knowledge on the objects' structure. We then consider these smaller bags to compare two objects both in a detailed perspective, stressing local matches between the smaller bags, and in a global or coarse perspective, by considering the entire bag. This multiresolution approach is likely to be best suited for tasks where the coarse approach is not precise enough, and where a more subtle mixture of both local and global similarities is necessary to compare objects. The approach presented here would not be computationally tractable without a factorization trick that we introduce before presenting promising results on an image retrieval task.