Related papers: Topologically Stable Hough Transform
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…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been…
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…
The persistent homology transform (PHT) represents a shape with a multiset of persistence diagrams parameterized by the sphere of directions in the ambient space. In this work, we describe a finite set of diagrams that discretize the PHT…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…
With the development of 3D sensing technologies, point clouds have attracted increasing attention in a variety of applications for 3D object representation, such as autonomous driving, 3D immersive tele-presence and heritage reconstruction.…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
We introduce a linear dimensionality reduction technique preserving topological features via persistent homology. The method is designed to find linear projection $L$ which preserves the persistent diagram of a point cloud $\mathbb{X}$ via…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
In this paper we introduce a statistic, the persistent homology transform (PHT), to model surfaces in $\mathbb{R}^3$ and shapes in $\mathbb{R}^2$. This statistic is a collection of persistence diagrams - multiscale topological summaries…