相关论文: Topological Brain Network Distances

The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular, the sublevel sets of the distance function are used in the computation of persistent homology -- a backbone of the…

This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…

Statistical analysis on non-Euclidean spaces typically relies on distances as the primary tool for constructing likelihoods. However, manifold-valued data admits richer structures in addition to Riemannian distances. We demonstrate that…

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Different types of graphs and complex networks have been characterized, analyzed, and modeled based on measurements of their respective topology. However, the available networks may constitute approximations of the original structure as a…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

The kinetic data structure (KDS) framework is a powerful tool for maintaining various geometric configurations of continuously moving objects. In this work, we introduce the kinetic hourglass, a novel KDS implementation designed to compute…

The training of neural networks is usually monitored with a validation (holdout) set to estimate the generalization of the model. This is done instead of measuring intrinsic properties of the model to determine whether it is learning…

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…

Accurate automatic brain tumor segmentation in Low and Middle-Income (LMIC) countries is challenging due to the lack of defined national imaging protocols, diverse imaging data, extensive use of low-field Magnetic Resonance Imaging (MRI)…

Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…

Graph Neural Networks (GNNs) are characterized by their capacity of processing graph-structured data. However, due to the sparsity of labels under semi-supervised learning, they have been found to exhibit biased performance on specific…

The problem of proposed topology for network comes when using Prim's algorithm with default distance (unrealistic distances) between network's nodes and don't care about the lakes, high hills, buildings, etc. This problem will cause…

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement…

While statistical analysis of a single network has received a lot of attention in recent years, with a focus on social networks, analysis of a sample of networks presents its own challenges which require a different set of analytic tools.…

Functional brain connectivity changes dynamically over time, making its representation challenging for learning on non-Euclidean data. We present a framework that encodes dynamic functional connectivity as an image representation of…

Graphs with heterophily have been regarded as challenging scenarios for Graph Neural Networks (GNNs), where nodes are connected with dissimilar neighbors through various patterns. In this paper, we present theoretical understandings of the…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…

Prediction the conversion to early-stage dementia is critical for mitigating its progression but remains challenging due to subtle cognitive impairments and structural brain changes. Traditional T1-weighted magnetic resonance imaging…