Related papers: Dynamic Topological Data Analysis of Functional Hu…

Topological Data Analysis (TDA) has emerged as a powerful framework for extracting robust and interpretable features from noisy high-dimensional data. In the context of Social Choice Theory, where preference profiles and collective…

Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…

Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks…

Despite the remarkable accuracies attained by machine learning classifiers to separate complex datasets in a supervised fashion, most of their operation falls short to provide an informed intuition about the structure of data, and, what is…

Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component…

We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize…

Autism Spectrum Disorder (ASD) is a prevalent neurological disorder. However, the multi-faceted symptoms and large individual differences among ASD patients are hindering the diagnosis process, which largely relies on subject descriptions…

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…

We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…