Related papers: A logifold structure on measure space

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…

A substantial volume of research has been devoted to studies of community structure in networks, but communities are not the only possible form of large-scale network structure. Here we describe a broad extension of community structure that…

Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the…

Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

In many applications, such as those arising from the field of cellular networks, it is often desired to determine the interaction (graph) structure of a set of differential equations, using as data measured sensitivities. This note proposes…

Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…

Based on an expert systems approach, the issue of community detection can be conceptualized as a clustering model for networks. Building upon this further, community structure can be measured through a clustering coefficient, which is…

Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…

Learning the right graph representation from noisy, multi-source data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…

Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work…

Domain generalization aims to learn a prediction model on multi-domain source data such that the model can generalize to a target domain with unknown statistics. Most existing approaches have been developed under the assumption that the…

It is common in the study of networks to investigate meso-scale features to try to gain an understanding of network structure and function. For example, numerous algorithms have been developed to try to identify "communities," which are…