Related papers: Cluster-Persistence for Weighted Graphs

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…

Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…

We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point…

In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction…

Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain complex with the goal of producing a persistence diagram…

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them,…

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

Persistent homology, an algebraic method for discerning structure in abstract data, relies on the construction of a sequence of nested topological spaces known as a filtration. Two-parameter persistent homology allows the analysis of data…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…

Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Recent findings underscore a substantial deterioration in the…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…