A subpath kernel for learning hierarchical image representations

International audienceTree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discrimi-native role. While such kernels have been successfully applied to various domains such as nature language processing and bioinformatics, they mostly concentrate on ordered trees and whose nodes are described by symbolic data. Meanwhile, hierarchical representations have gained increasing interest to describe image content. This is particularly true in remote sensing, where such representations allow for revealing different objects of interest at various scales through a tree structure. However, the induced trees are unordered and the nodes are equipped with numerical features. In this paper, we propose a new structured kernel for hierarchical image representations which is built on the concept of subpath kernel. Experimental results on both artificial and remote sensing datasets show that the proposed kernel manages to deal with the hierarchical nature of the data, leading to better classification rates

Linear-time algorithms for the subpath kernel

The subpath kernel is a useful positive definite kernel, which takes arbitrary rooted trees as input, no matter whether they are ordered or unordered, We first show that the subpath kernel can exhibit excellent classification performance in combination with SVM through an intensive experiment. Secondly, we develop a theory of irreducible trees, and then, using it as a rigid mathematical basis, reconstruct a bottom-up linear-time algorithm for the subtree kernel, which is a correction of an algorithm well-known in the literature. Thirdly, we show a novel top-down algorithm, with which we can realize a linear-time parallel-computing algorithm to compute the subpath kernel