Ordered Decompositional DAG kernels enhancements

Ordered Decompositional DAG kernels enhancements

In this paper, we show how the Ordered Decomposition DAGs (ODD) kernel framework, a framework that allows the definition of graph kernels from tree kernels, allows to easily define new state-of-the-art graph kernels. Here we consider a fast graph kernel based on the Subtree kernel (ST), and we propose various enhancements to increase its expressiveness. The proposed DAG kernel has the same wors...

Kernels for sequentially ordered data

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a “sequentialized” version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are...

On the Regularity and Learnability of Ordered DAG Languages

Order-Preserving DAG Grammars (OPDGs) is a subclass of Hyper-Edge Replacement Grammars that can be parsed in polynomial time. Their associated class of languages is known as Ordered DAG Languages, and the graphs they generate are characterised by being acyclic, rooted, and having a natural order on their nodes. OPDGs are useful in natural-language processing to model abstract meaning representa...

Voronoi Order Skeletons and Dag-ordered Trees: a System for Mpeg-7 Shape Query

Decompositional Modeling through Caricatural Reasoning

Many physical phenomena are suuciently complex that the corresponding equations aaord little insight, or no analytical method provides an exact solution. Decompositional modeling (DM) captures a modeler's tacit skill at solving non-linear algebraic systems. DM divides statespace into a patchwork of simpler subregimes, called caricatures, each of which preserves only the dominant characteristics...