Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
problem Finding upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
method Using spectral decompositions and consistency conditions derived from quadruple overlap integrals in terms of triple overlap integrals.
result Derives upper bounds on eigenvalues, nearly saturated by the Bolza surface.
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.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
New spectral clustering method handles discrete covariates for better community detection.
problem Community detection in networks with discrete covariates.
method Spectral algorithm that separates latent network structure from observed covariates.
result Achieves perfect clustering with high probability in large, sparse networks.
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.
problem Improving spectral embedding for multipartite networks to better represent node types.
method Developed a follow-on step to spectral embedding that recovers node representations in their intrinsic rather than ambient dimension, proving consistency under a specific model.
result Node representations in multipartite networks lie near type-specific subspaces, and the proposed method recovers these representations consistently.
Consistent spectral clustering with fairness constraints on representation graphs.
problem Finding balanced clusters in similarity graphs with fairness constraints.
method Developed variants of unnormalized and normalized spectral clustering for fair planted partitions.
result Consistency results for constrained spectral clustering under fair planted partitions.
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…
The paper improves spectral convergence rates for graph Laplacians.
problem Improving spectral convergence rates for graph Laplacians.
method Utilizing regularity of continuum eigenfunctions and strong pointwise consistency results.
result Eigenvalues and eigenvectors of graph Laplacian converge to continuum at rate O(n−1/(m+4)). New method shows spectral clustering is consistent with theoretical guarantees.
problem Lack of theoretical support for anchor-based spectral clustering.
method Defined and analyzed a specific anchor-based algorithm.
result Theoretical consistency of the method in asymptotic settings.
New framework detects directional influence in multivariate time series.
problem Detecting directional influence in multivariate time series.
method Order-constrained spectral non-invariance.
result Unique diagnostic functional for directional influence.
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×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.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random k-nearest neighbor graph. result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
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 RD, we establish the spectral convergence rate…
New algorithms improve community detection in network data with strong consistency.
problem Challenges in effectively adapting spectral clustering techniques and achieving strong consistency in label recovery.
method Proposed Thresholded Cosine Spectral Clustering (TCSC) and one-step Refined TCSC algorithms, with strong consistency proofs.
result One-step Refined TCSC achieves strong consistency in community detection under PABM, correctly recovering all labels with high probability.
Spectral algorithm recovers community structure in sparse hypergraphs.
problem Community detection in sparse random hypergraphs with community structure and higher-order interactions.
method Spectral algorithm with three steps: hyperedge selection, spectral partition, and correction/merging.
result Weak consistency achieved for weak signal-to-noise ratio.
A new UNet variant reduces spectral artifacts in image transformations.
problem Spectral artifacts caused by traditional UNet upsampling layers.
method Introduced a Guided UNet (GUNet) architecture using a novel upsampling module.
result GUNet produces higher fidelity outputs 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.
problem Community recovery in dense geometric graphs.
method Spectral clustering algorithm using eigenvectors of adjacency matrix.
result Strong consistency in community recovery proved.
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.
problem Challenges in extracting meaningful peaks from noisy or complex spectra.
method Bayesian spectral deconvolution coupled with a physical-property regression layer.
result Recovery of weak peaks in poly(lactic acid) IR spectra related to degradation rates.
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.
problem Consistency of spectral clustering on hierarchical stochastic block models.
method Recursive bi-partitioning algorithm based on Fiedler vector of graph Laplacian.
result Strong consistency of the method under various model parameters.
The paper studies Hodge Laplacians from point clouds, proving spectral convergence and harmonic form consistency.
problem Analyzing Riemannian submanifolds from point cloud data.
method Constructing deformed Hodge Laplacians and empirical operators from point clouds, proving convergence properties.
result Empirical spectral cluster contains the k-th Betti number and converges to harmonic k-forms. Study confirms learning rates for vector-valued spectral algorithms, proving consistency.
problem Theoretical confirmation of learning rates for vector-valued spectral algorithms.
method Rigorous analysis of learning rates for various vector-valued spectral algorithms, including kernel ridge regression and gradient descent.
result Upper and lower bounds on learning rates for vector-valued spectral algorithms, proving minimax optimality in various scenarios.
Improved spectral clustering guarantees for dynamic stochastic block models.
problem Analyzing Spectral Clustering in dynamic stochastic block models.
method Extending guarantees to sparse and smooth DSBM, linking sparsity and smoothness.
result Improved error bounds for consistent recovery in dynamic DSBM.
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…
A new training method for GANs improves image generation quality.
problem Training GANs is challenging and unstable.
method Consistency regularization to stabilize GAN training.
result CR-GAN achieves best FID scores for unconditional image generation.
This paper proposes a spectral clustering algorithm for hyperbolic spaces, improving efficiency over Euclidean methods.
problem Inefficient clustering in Euclidean spaces for complex data structures.
method Developed a spectral clustering algorithm using hyperbolic similarity matrices.
result The algorithm converges at least as fast as Euclidean spectral clustering and performs better on complex datasets.
A 3-stage method enhances hyperspectral image classification accuracy.
problem Classifying detailed classes in hyperspectral images with limited labeled data.
method Uses Nested Sliding Window and PCA for spatial consistency, SVM for spectral estimation, and TV model for spatial smoothing.
result Our method outperforms state-of-the-art algorithms, especially in scenarios with small training sets.
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.
problem Estimating distances in compact Riemannian manifolds.
method Graph Laplacian estimates of the Laplace-Beltrami operator, bounding errors.
result Proof of consistency for manifold distances.
Spectral clustering with edge counting detects communities in sparse models.
problem Detecting communities in sparse latent space models.
method Spectral clustering followed by edge counting.
result Algorithm achieves consistency and optimality for a broad class of models.
New method filters large networks from financial data to reveal key subnetworks.
problem Filtering large dimensional networks to isolate key constituents.
method Exploits spectral properties of high-dimensional data networks, tuning for sparsity and consistency.
result Shows method can interpolate between zero and maximal filtering, preserving spectral properties.
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…
Proposes a new framework for risk-sensitive RL using deep nets.
problem Risk-sensitive reinforcement learning problems.
method Conditional elicitability, scoring functions, deep neural networks.
result Dynamic spectral risk measures can be approximated by deep nets.
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…
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…
New method finds balanced clusters in graphs using auxiliary information.
problem Finding balanced clusters in graphs with population-level constraints.
method Proposes individual-level balancing constraint and develops spectral clustering algorithms.
result Establishes first statistical consistency result for constrained spectral clustering.
Spectral clustering is robust to helpful model changes but not to random changes.
problem Robustness of spectral clustering in the presence of semirandom adversaries.
method Analysis of spectral clustering algorithms under semirandom adversaries.
result Spectral clustering with unnormalized Laplacian is strongly consistent under semirandom adversaries.
New Bethe-Hessian method improves community detection in sparse networks.
problem Detect communities in sparse networks efficiently.
method Spectral clustering using the Bethe-Hessian matrix.
result Bethe-Hessian consistently estimates block number above Kesten-Stigum threshold.
Dual regularized graph Laplacian improves spectral clustering for community detection.
problem Detecting clusters in networks with improved spectral clustering methods.
method Proposes dual regularized graph Laplacian for three spectral clustering approaches.
result Theoretical analysis shows DRSC and DRSLIM yield stable consistent community detection.
A new method for community detection in networks is presented.
problem Community detection in network analysis.
method Mixed regularized spectral clustering (Mixed-RSC) based on the regularized Laplacian matrix.
result The method is asymptotically consistent under mild conditions.
Paper proposes a forecasting model combining autoregressive models with spectral attention.
problem Time series forecasting across various domains.
method Combines deep autoregressive models with Spectral Attention (SA) module.
result SAAM consistently demonstrates improved forecasting accuracy compared to state-of-the-art approaches.