Related papers: Flexible and Probabilistic Topology Tracking with …

In this paper we provide a novel mathematical optimization based methodology to perturb the features of a given observation to be re-classified, by a tree ensemble classification rule, to a certain desired class. The method is based on…

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…

We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes…

The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location…

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…

Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

Conventional cell tracking methods detect multiple cells in each frame (detection) and then associate the detection results in successive time-frames (association). Most cell tracking methods perform the association task independently from…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

In this work we define a metric structure to compare functions defined on different merge trees. The metric introduced possesses some stability properties, which we illustrate within a standard topological data analysis (TDA) framework, and…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Many problems in dynamic data driven modeling deals with distributed rather than lumped observations. In this paper, we show that the Monge-Kantorovich optimal transport theory provides a unifying framework to tackle such problems in the…

This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from…

Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…

We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…

Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on…

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…

We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…