Related papers: Splay Top Trees
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…
We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a structure that is desirable in many aspects. While much…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
Modern graphs are both large and dynamic, presenting significant challenges for fundamental queries, such as the Single-Source Shortest Path (SSSP) problem. Naively recomputing the SSSP tree after each topology change is prohibitively…
Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for…
The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…