Related papers: Topological Data Analysis for Multivariate Time Se…
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes…
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the performance of machine learning models. Deeply rooted in algebraic topology, persistent…
Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…
Recently, deep learning (DL) approaches to vulnerability detection have gained significant traction. These methods demonstrate promising results, often surpassing traditional static code analysis tools in effectiveness. In this study, we…
This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex…
Recent years have witnessed a fast growth in mathematical artificial intelligence (AI). One of the most successful mathematical AI approaches is topological data analysis (TDA) via persistent homology (PH) that provides explainable AI (xAI)…
We present a topological framework for analysing neural time series that integrates Transfer Entropy (TE) with directed Persistent Homology (PH) to characterize information flow in spiking neural systems. TE quantifies directional influence…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…
The analysis of nonlinear dynamics is an important issue in numerous fields of science. In this study, we propose a new method to analyze the time series data using persistent homology (PH). The key idea is the application of PH to the…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Understanding how individuals navigate mental health challenges over time is critical yet methodologically challenging. Traditional approaches analyze community-level snapshots, failing to capture dynamic individual recovery trajectories.…
We propose a novel exact multi-parameter persistent homology method for analyzing time-series data utilizing the Liouville torus. In the field of topological data analysis (TDA), the conventional approach to analyzing time-series data often…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
Understanding how the brain represents and processes information is crucial for advancing neuroscience and artificial intelligence. Representational similarity analysis (RSA) has been instrumental in characterizing neural representations,…
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information…
We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological…
In recent years, graph neural networks (GNNs) have emerged as a potent tool for learning on graph-structured data and won fruitful successes in varied fields. The majority of GNNs follow the message-passing paradigm, where representations…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Bearing fault detection is a critical task in predictive maintenance, where accurate and timely fault identification can prevent costly downtime and equipment damage. Traditional attention mechanisms in Transformer neural networks often…