Related papers: Flexible and Probabilistic Topology Tracking with …
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical…
This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
In this work, we introduce an optimal transport framework for inferring power distributions over both spatial location and temporal frequency. Recently, it has been shown that optimal transport is a powerful tool for estimating spatial…
We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral…
We present a holistic, topology-based visualization technique for spatial time series data based on an adaptation of Fuzzy Contour Trees. Common analysis approaches for time dependent scalar fields identify and track specific features. To…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
Merge trees are a common topological descriptor for data with a hierarchical component, such as terrains and scalar fields. The interleaving distance, in turn, is a common distance for comparing merge trees. However, the interleaving…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…
Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical…
Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…