Related papers: On the Bootstrap for Persistence Diagrams and Land…
Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning.…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string…
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence…
Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…