Related papers: An Application of Topological Data Analysis to Hoc…

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…

American football is unique in that offensive and defensive units typically consist of separate players who don't share the field simultaneously, which tempts one to evaluate them independently. However, a team's offensive and defensive…

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

During the past few years advancements in sports information systems and technology has allowed us to collect a number of detailed spatio-temporal data capturing various aspects of basketball. For example, shot charts, that is, maps…

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the…

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…

In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in…

The surge of data available on the Internet has driven the adoption of a wide range of computational methods for analyzing and extracting insights from large-scale data. Among these, Machine Learning (ML) has become a central paradigm,…

Esport games comprise a sizeable fraction of the global games market, and is the fastest growing segment in games. This has given rise to the domain of esports analytics, which uses telemetry data from games to inform players, coaches,…

The goal of this paper is to develop an adjusted plus-minus statistic for NHL players that is independent of both teammates and opponents. We use data from the shift reports on NHL.com in a weighted least squares regression to estimate an…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various…

Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…

Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…

The global sports analytics industry has a market value of USD 3.78 billion in 2023. The increase of wearables such as GPS sensors has provided analysts with large fine-grained datasets detailing player performance. Traditional analysis of…

This work investigates the problem of multi-agents trajectory prediction. Prior approaches lack of capability of capturing fine-grained dependencies among coordinated agents. In this paper, we propose a spatial-temporal trajectory…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…