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.
New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.
Study uses graph Laplacians to analyze surface links.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
Enhances clustering performance with a novel high-order Laplacian matrix.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
New nodal domain theorems for symmetric matrices via signed graphs.
New random feature maps for Laplacian and related kernels.
New method clusters hypergraphs using weighted random walks and Laplacians.
Paper optimizes Laplacian regularization for sparse network clustering.
Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…
New methods link Calabi-Yau metrics to random matrices.
Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.
We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate, but related, subpopulations, while allowing for differences among matrices. We p…
Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noi…
Study shows rates for Laplacian-eigenmap methods in nonparametric regression.
The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Ale…
Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms. When suitably scaled, graph Laplacians approach limiting cont…
New curvature tensor and matrices for connection graphs derived from Bakry-Émery curvature.
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs can in turn be represented by matrices. A special example is the Laplacian matr…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretatio…
Random surfaces have a strong spectral gap with polynomial rate.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, ) is generally unknown a-priori. Consequently, the majority of t…
The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.
The smallest eigenvectors of the graph Laplacian are well-known to provide a succinct representation of the geometry of a weighted graph. In reinforcement learning (RL), where the weighted graph may be interpreted as the state transition process induced by a behavior policy acting on the environment, approximating the …
This paper explains spectral clustering and its equivalence to PCA, breaking it into fully connected and multi-connected cases.
This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. The conformally invariant powers of the Laplacian arise as residues of the scattering matrix and Branson's Q-curvature in even dimen…
New method detects structural shifts in multivariate Hawkes processes.
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter…
The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. Firs…
We consider families of degenerating hyperbolic surfaces. The surfaces are geometrically finite of fixed topological type. Let Z(s) be the Selberg Zeta function of a surface, and let Z_d(s) be the contribution of the pinched geodesics to the Zeta function. Extending a result of Hejhal and Wolpert, we prove that the quo…
Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the n…
Study on signed graphs with random signs, focusing on community detection.
A fast metric learning framework using Gershgorin disc alignment.
Paper proposes a method to improve graph clustering by integrating node textual metadata with node signals in GGMs.
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the or…
Proposes a method to infer complex network topologies from multiple graphs.
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…
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard graph-theoretic properties, such as the degree and eigenvalue di…
Paper introduces a taxonomy of reduction matrices for more efficient graph coarsening.
Unified framework detects overfitting in crash classification models.
AGE improves graph embedding by smoothing features and iteratively enhancing node embeddings.
New centrality-based graph shift operators improve graph neural networks.
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field. This is the first generative model of its kind for directed graphs. We introduce…
Improved spectral clustering guarantees for dynamic stochastic block models.