Related papers: Cluster-Persistence for Weighted Graphs
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
Persistent homology has been widely used to study the topology of point clouds in $\mathbb{R}^n$. Standard approaches are very sensitive to outliers, and their computational complexity depends badly on the number of data points. In this…
In this paper, we introduce a novel unsupervised, graph-based filter feature selection technique which exploits the power of topologically constrained network representations. We model dependency structures among features using a family of…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals,…
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here…
In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
Clustering nodes in heterophilous graphs is challenging as traditional methods assume that effective clustering is characterized by high intra-cluster and low inter-cluster connectivity. To address this, we introduce HeNCler-a novel…
This work aims at improving the quality of structural variant prediction from the mapped reads of a sequenced genome. We suggest a new model based on cluster editing in weighted graphs and introduce a new heuristic algorithm that allows to…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…