Related papers: STruD: Truss Decomposition of Simplicial Complexes
Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…
The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional…
Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…
Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…
In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
The structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data. In this paper, we propose nearest prime simplicial complex approaches (NSC) by utilizing persistent…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
Spatiotemporal modeling has evolved beyond simple time series analysis to become fundamental in structural time series analysis. While current research extensively employs graph neural networks (GNNs) for spatial feature extraction with…
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes…
We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…
A structural graph summary is a small graph representation that preserves structural information necessary for a given task. The summary is used instead of the original graph to complete the task faster. We introduce multi-view structural…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid…
Finding dense components in graphs is of great importance in analyzing the structure of networks. Popular and computationally feasible frameworks for discovering dense subgraphs are core and truss decompositions. Recently, Sariyuce et al.…
It is known that any chordal graph on $n$ vertices can be represented as the intersection of $n$ subtrees in a tree on $n$ nodes. This fact is recently used in [2] to generate random chordal graphs on $n$ vertices by generating $n$ subtrees…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…
Hypergraphs and simplical complexes both capture the higher-order interactions of complex systems, ranging from higher-order collaboration networks to brain networks. One open problem in the field is what should drive the choice of the…