Related papers: Dynamic Topological Data Analysis of Functional Hu…

Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…

We introduce PH-STAT, a comprehensive MATLAB toolbox designed for performing a wide range of statistical inferences and machine learning tasks on persistent homology, primarily for network and graph data, with an emphasis on brain network…

At present, the vast majority of human subjects with neurological disease are still diagnosed through in-person assessments and qualitative analysis of patient data. In this paper, we propose to use Topological Data Analysis (TDA) together…

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

This work introduces a novel framework for testing topological variability in weighted networks by combining Hodge decomposition with Wasserstein variance minimization. Traditional approaches that analyze raw edge weights are susceptible to…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…

Artificial Neural Networks (ANNs) require significant amounts of data and computational resources to achieve high effectiveness in performing the tasks for which they are trained. To reduce resource demands, various techniques, such as…

Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…

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,…

Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…

In the context of rapid urbanization, understanding the patterns of urban residents' activities and mobility is crucial for optimizing transportation systems and enhancing urban management efficiency. This study addresses the limitations of…

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…

A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…

Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…