Related papers: Dynamic Topological Data Analysis of Functional Hu…
We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised…
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…
Continual learning in neural networks suffers from a phenomenon called catastrophic forgetting, in which a network quickly forgets what was learned in a previous task. The human brain, however, is able to continually learn new tasks and…
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…
The formation of transient networks in response to external stimuli or as a reflection of internal cognitive processes is a hallmark of human brain function. However, its identification in fMRI data of the human brain is notoriously…
We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…
High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an…
Network science has become an essential interdisciplinary tool for understanding complex biological systems. However, because these systems undergo continuous, often stimulus-driven changes in both structure and function, traditional static…
Brain network provides important insights for the diagnosis of many brain disorders, and how to effectively model the brain structure has become one of the core issues in the domain of brain imaging analysis. Recently, various computational…
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates,…
In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application, we perform binary and ternary classification tasks on two public datasets that consist of physiological…
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…
Graph Neural Networks (GNNs) are widely used for node classification tasks but often fail to generalize when training and test nodes come from different distributions, limiting their practicality. To overcome this, recent approaches adopt…
Understanding the structure of the brain, and how it changes with time and disease, is a core goal of structural neuroimaging. Contemporary approaches to structural brain analysis are dominated by voxel-wise, mass-univariate methods such as…
Topological data analysis has recently been applied to the study of dynamic networks. In this context, an algorithm was introduced and helps, among other things, to detect early warning signals of abnormal changes in the dynamic network…
In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in various areas such as science, politics, economy, healthcare,…
Understanding brain dynamics through functional Magnetic Resonance Imaging (fMRI) remains a fundamental challenge in neuroscience, particularly in capturing how the brain transitions between various functional states. Recently,…
Now that disease-modifying therapies for Alzheimer disease have been approved by regulatory agencies, the early, objective, and accurate clinical diagnosis of AD based on the lowest-cost measurement modalities possible has become an…
Topological data analysis (TDA) is a rising field in the intersection of mathematics, statistics, and computer science/data science. The cornerstone of TDA is persistent homology, which produces a summary of topological information called a…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…