Related papers: Topologically Invariant Permutation Test
Deep neural networks are applied in more and more areas of everyday life. However, they still lack essential abilities, such as robustly dealing with spatially transformed input signals. Approaches to mitigate this severe robustness issue…
Persistent Topology studies topological features of shapes by analyzing the lower level sets of suitable functions, called filtering functions, and encoding the arising information in a parameterized version of the Betti numbers, i.e. the…
We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is a homotopy classification, which enables us to see more topological invariants.…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
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…
Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being…
Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of…
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…
Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study performs whole-brain…
Topology identification (TI) in distribution networks is a challenging task due to the limited measurement resources and therefore the inevitable need to use pseudo-measurements that are often inaccurate. To address this issue, a new method…
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little…
Persistent homology (PH) is a crucial concept in computational topology, providing a multiscale topological description of a space. It is particularly significant in topological data analysis, which aims to make statistical inference from a…
Functional Magnetic Resonance Imaging (fMRI) is commonly utilized to study human brain activity, including abnormal functional properties related to neurodegenerative diseases. This study aims to investigate the differences in the…
The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose…
In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…