Related papers: Medians of populations of persistence diagrams
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data. The use of machine learning algorithms on the space of persistence diagrams proves to…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
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.…
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…
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 --…
Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a…
Persistence diagrams are two-dimensional plots that summarize the topological features of functions and are an important part of topological data analysis. A problem that has received much attention is how deal with sets of persistence…
Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series or point clouds sampled close to a manifold. Given random…
Topological Data Analysis (TDA) provides a toolkit for the study of the shape of high dimensional and complex data. While operating on a space of persistence diagrams is cumbersome, persistence norms provide a simple real value measure of…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…