Related papers: A tool for filtering information in complex system…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by…
We propose a network-filtering method, the Triangulated Maximally Filtered Graph (TMFG), that provides an approximate solution to the Weighted Maximal Planar Graph problem. The underlying idea of TMFG consists in building a triangulation…
In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…
Multi-relational clustering is a challenging task due to the fact that diverse semantic information conveyed in multi-layer graphs is difficult to extract and fuse. Recent methods integrate topology structure and node attribute information…
We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are…
Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…
Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a…
This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
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…
The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation…
In this work, we introduce a filtration on temporal graphs based on $\delta$-temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered…
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph. Various definitions and motivations for these weights are given. The detection of…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
Graph-based collaborative filtering methods have prevailing performance for recommender systems since they can capture high-order information between users and items, in which the graphs are constructed from the observed user-item…