相关论文: New divergence measures between persistence diagra…

Comparative visualization of scalar fields is often facilitated using similarity measures such as edit distances. In this paper, we describe a novel approach for similarity analysis of scalar fields that combines two recently introduced…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…

We consider synthesis and analysis of probability measures using the entropy-regularized Wasserstein-2 cost and its unbiased version, the Sinkhorn divergence. The synthesis problem consists of computing the barycenter, with respect to these…

Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…

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…

We introduce a new one-parameter family of divergence measures, called bounded Bhattacharyya distance (BBD) measures, for quantifying the dissimilarity between probability distributions. These measures are bounded, symmetric and positive…

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…

Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…

This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…

This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…

Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…

Single-parameter persistent homology, a key tool in topological data analysis, has been widely applied to data problems along with statistical techniques that quantify the significance of the results. In contrast, statistical techniques for…

The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…

In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate…

The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…