Related papers: Interactive Visualization of 2-D Persistence Modul…
The fibered barcode $\mathcal{F}(M)$ of a bipersistence module $M$ is the map sending each non-negatively sloped affine line $\ell \subset \mathbb{R}^2$ to the barcode of the restriction of $M$ along $\ell$. The simplicity, computability,…
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…
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules…
Time-series of persistence diagrams, known as vineyards, have shown to be useful in diverse applications. A natural algebraic version of vineyards is a time series of persistence modules equipped with interleaving maps between the…
Sophisticated visualization tools are essential for the presentation and exploration of human neuroimaging data. While two-dimensional orthogonal views of neuroimaging data are conventionally used to display activity and statistical…
Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…
Constructing latent vector representation for nodes in a network through embedding models has shown its practicality in many graph analysis applications, such as node classification, clustering, and link prediction. However, despite the…
Motivated by applications to topological data analysis, we give an efficient algorithm for computing a (minimal) presentation of a bigraded $K[x,y]$-module $M$, where $K$ is a field. The algorithm takes as input a short chain complex of…
Multi-parameter persistent homology naturally arises in applications of persistent topology to data that come with extra information depending on additional parameters, like for example time series data. We introduce the concept of a…
Persistent Homology (PH) is a useful tool to study the underlying structure of a data set. Persistence Diagrams (PDs), which are 2D multisets of points, are a concise summary of the information found by studying the PH of a data set.…
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…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of…
Interactive visualization is a common tool for exploring large open-data repositories, where users quickly explore datasets across diverse domains. When it comes to large-scale spatial data, many existing tools rely on server-side rendering…
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…
The Persint program is designed for the three-dimensional representation of objects and for the interfacing and access to a variety of independent applications, in a fully interactive way. Facilities are provided for the spatial navigation…
The Rivet toolkit is the primary mechanism for phenomenological preservation of collider-physics measurements, containing both a computational core and API for analysis implementation, and a large collection of more than a thousand…
We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to the underlying neighbourhood graph and percolating the…
Salient object detection (SOD) on RGB and depth images has attracted more and more research interests, due to its effectiveness and the fact that depth cues can now be conveniently captured. Existing RGB-D SOD models usually adopt different…