arXiv research

Enhanced spectral clustering for geometric graphs improves clustering accuracy.

The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.

For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…

Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.

New spectral clustering method handles discrete covariates for better community detection.

Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…

This paper improves spectral embedding for multipartite networks, revealing latent subspaces and providing consistent node representations.

Consistent spectral clustering with fairness constraints on representation graphs.

We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…

New method shows spectral clustering is consistent with theoretical guarantees.

New framework detects directional influence in multivariate time series.

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the…

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading eigenvectors, where $k$ is the desired number of clusters among $n$ objects. This is pro…

Spectral clustering identifies clusters of multivariate extremes.

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm…

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

New algorithms improve community detection in network data with strong consistency.

Spectral algorithm recovers community structure in sparse hypergraphs.

A new UNet variant reduces spectral artifacts in image transformations.

We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these "intermediate fusion" methods involve obtaining a low column rank matr…

Spectral clustering for geometric graphs achieves strong consistency in community recovery.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.

Spectral images captured by satellites and radio-telescopes are analyzed to obtain information about geological compositions distributions, distant asters as well as undersea terrain. Spectral images usually contain tens to hundreds of continuous narrow spectral bands and are widely used in various fields. But the vast…

Study proves consistency of spectral clustering on hierarchical networks.

The paper studies Hodge Laplacians from point clouds, proving spectral convergence and harmonic form consistency.

Study confirms learning rates for vector-valued spectral algorithms, proving consistency.

In this work we prove that every locally symmetric smooth submanifold gives rise to a naturally defined smooth submanifold of the space of symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs to the locally symmetric manifold. We also present an explicit f…

This paper proposes a spectral clustering algorithm for hyperbolic spaces, improving efficiency over Euclidean methods.

A 3-stage method enhances hyperspectral image classification accuracy.

We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to perform optimally both theoretically using asymptotic theory and empirically.

Estimates manifold distances using graph Laplacian, proving consistency.

Spectral clustering with edge counting detects communities in sparse models.

New method filters large networks from financial data to reveal key subnetworks.

We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. The spectral algorithm consists of multiple algorithmic steps, named as "{edges}", to which noise cou…

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…

Proposes a new framework for risk-sensitive RL using deep nets.

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustere…

In the traditional framework of spectral learning of stochastic time series models, model parameters are estimated based on trajectories of fully recorded observations. However, real-world time series data often contain missing values, and worse, the distributions of missingness events over time are often not independe…

In this paper we improve the spectral convergence rates for graph-based approximations of Laplace-Beltrami operators constructed from random data. We utilize regularity of the continuum eigenfunctions and strong pointwise consistency results to prove that spectral convergence rates are the same as the pointwise consist…

New method finds balanced clusters in graphs using auxiliary information.

Spectral clustering is robust to helpful model changes but not to random changes.

New Bethe-Hessian method improves community detection in sparse networks.

Dual regularized graph Laplacian improves spectral clustering for community detection.

A new method for community detection in networks is presented.

Paper proposes a forecasting model combining autoregressive models with spectral attention.

A Python package solves source duplication in single channel LVMs using spectral regularisation.

A new method for nonstationary Gaussian processes using Fourier features.