Ordered Decompositional DAG kernels enhancements

A Tree-Based Kernel for Graphs

This paper proposes a new tree-based kernel for graphs. Graphs are decomposed into multisets of ordered Directed Acyclic Graphs (DAGs) and a family of kernels computed by application of tree kernels extended to the DAG domain. We focus our attention on the efficient development of one member of this family. A technique for speeding up the computation is given, as well as theoretical bounds and ...

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...

When the Whole Is Not Greater Than the Combination of Its Parts: A "Decompositional" Look at Compositional Distributional Semantics

Distributional semantics has been extended to phrases and sentences by means of composition operations. We look at how these operations affect similarity measurements, showing that similarity equations of an important class of composition methods can be decomposed into operations performed on the subparts of the input phrases. This establishes a strong link between these models and convolution ...

The Last Formula of Jacques-louis Lions: Reproducing Kernels for Harmonic and Other Functions

Ordered Dags: HypercubeSort

We generalise the insertion into a binary heap to any directed acyclic graph (DAG) with one source vertex. This lets us formulate a general method for converting any such DAG into a data structure with priority queue interface. We apply our method to a hypercube DAG to obtain a sorting algorithm of complexity $\mathcal{O}(n\log^2 (n))$. As another curious application, we derive a relationship b...