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.
The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
Spectral sparsification improves Laplacian-constrained graph learning.
We provide a theoretical analysis of the representation learning problem aimed at learning the latent variables (design matrix) of observations with the knowledge of the coefficient matrix . The design matrix is learned under the assumption that the latent variables are smooth with respect to a (known) t…
Unified spectral clustering for sparse networks with heterogeneous degrees.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
GS-BSE improves label shift estimation by smoothing priors on a graph.
Transformers interpreted as probabilistic Laplacian Eigenmaps steps.
Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.
New algorithms detect and estimate rank-one signals with prior directional information.
Enhances clustering performance with a novel high-order Laplacian matrix.
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
The paper tackles sparse graph learning under Laplacian-related constraints, improving upon existing methods.
The paper explores learning graphs in financial markets using Laplacian constraints.
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…
New outlier detection method using graph Laplacian spectrum boosts performance.
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…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
The -norm fails to produce sparse solutions in Laplacian constrained graphical models, leading to a complete graph.
S2MAM improves semi-supervised learning by selecting relevant variables and updating similarity metrics.
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…
In this paper we study the heat equation (of Hodge-Laplacian) deformation of -forms on a Kähler manifold. After identifying the condition and establishing that the positivity of a -form solution is preserved under such an invariant condition we prove the sharp differential Harnack (in the sense of Li-Ya…
New theory for eigenvectors of generalized Laplacian matrices, addressing dependency issues.
Study on signed graphs with random signs, focusing on community detection.
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacia…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for 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 …
Novel Haar-Laplacian for directed graphs enhances spectral graph applications.
We consider worker skill estimation for the single-coin Dawid-Skene crowdsourcing model. In practice, skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completi…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be investigated via the spectrum of the Hessian of the empirical loss function. Networ…
We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimiz…
Dual regularized graph Laplacian improves spectral clustering for community detection.
The paper develops a method to sparsify magnetic Laplacians using multi-type spanning forests.
New invariant for special alternating links based on graph Laplacian.
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank factorizations in order to approximately decompose and eventually invert such big…
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…
The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a ha…
The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LM…
Study conic Laplacian on \(\mb P^1\) with explicit model and boundary data.
Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface and compute the -matrix of at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian…
LEGO estimates tangent spaces more robustly than LPCA in noisy data.
We prove a central limit theorem for the components of the eigenvectors corresponding to the largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two step…
Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date, little work has been done to investigate the tradeoff between computational resourc…
The paper proves spectral convergence rates for graph Laplacian to manifold Laplace-Beltrami operator.
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
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…
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results obtained earlier for the scalar Laplacian and present closed formulas for all heat in…