A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-fr…
New outlier detection method using graph Laplacian spectrum boosts performance.
In this paper, we consider three typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. We use the Bochner formula to derive the Bernstein type estimate of the heat equation. The second is to derive the Reilly t…
Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.
New graph convolution captures local features on non-Euclidean grids.
In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack's inequality for positive solutions of the Schrodinger equations. We also set up some results about Green functions of the Laplacian equation on locally finite graph. Interesting …
Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we …
We study the existence and uniqueness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a uniqueness criterion, shown to be optimal, is given in terms of the maximal valence on spheres about a fixed vertex. A sufficient condition for non-uniqueness is also presented. Furthermore, we …
Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian regularization framework, GCNs perform an implicit Laplacian type regularization to …
The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for capturing local and global geometry in many classes of learning problems, and the tec…
In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a sufficient condition for stochastic completeness is given in terms of the maximum vale…
Study -parabolicity on graphs using various energy functionals.
Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intu…
Extends manifold learning to non-Euclidean metrics.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
Study shows SNN graph Laplacians converge to k-NN graph Laplacians under large scale asymptotics.
This work improves GNN training efficiency by maximizing ego-graph information.
Paper learns Cartesian product graphs with Laplacian constraints.
The paper compares Steklov and Laplacian eigenvalues on graphs.
New methods identify local clusters in graphs with few labels.
The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and explicitly allow infinite graphs. Motivated by the general form of a Laplacian on …
Spectral sparsification improves Laplacian-constrained graph learning.
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…
In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally finite connected graph with Ricci curvature lower bounds. Furthermore, we derive that the graph with positive curvature is finite, especially…
We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construc…
Improved convergence rate for kNN graph Laplacians with adaptive bandwidth.
The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.
Paper proves convergence of bi-stochastically normalized graph Laplacian to manifold Laplacian and robustness to outlier noise.
Paper describes eigenvalues of genus 3 surfaces graphs.
Develops methods to analyze manifold singularities using graph Laplacian.
Network Lasso clusters sparse graph clusters efficiently.
Study spectral properties of graph Laplacian for manifold data.
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by the orthonormal basis for the graph Laplacian, they suffer from hig…
We study ancient solutions of polynomial growth to both continuous-time and discrete-time heat equations on graphs with unbounded Laplacians. We generalize Colding and Minicozzi's theorem [CM19] on manifolds, and the result [Hua19] on graphs with normalized Laplacians to the setting of graphs with unbounded Laplacians:…
New regularization techniques improve stability of deep neural networks.
Graph poly-Laplacian method improves regression accuracy.
Propagation-regularization improves GNN performance by infusing extra graph information.
New method clusters evolving networks using spatio-temporal graph Laplacian.
Study Hodge Laplacians for manifold data, improving error bounds.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
New curvature tensor and matrices for connection graphs derived from Bakry-Émery curvature.
A sign is introduced in the usual Laplacian on graphs and the corresponding analogue of the isoperimetric constant for this Laplacian is presented, i.e. a geometric quantity which enables to bound from above and below the first eigenvalue. The introduction of the sign in the Laplacian is motivated by the study of -l…
BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.
New method learns high-quality Laplacian representations for reinforcement learning.