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.
Improved spectral clustering for community detection in networks.
problem Community detection in networks.
method Improved spectral clustering (ISC) based on k-means clustering on weighted eigenvectors of a regularized Laplacian matrix.
result ISC yields stable consistent community detection under mild conditions and outperforms classical methods.
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 spectral method for community detection in complex networks.
problem Community detection in heterogeneous large networks.
method Spectral methods based on α-parametrized normalized modularity matrix, with regularization of eigenvectors.
result Existence of an optimal value α_opt for best community detection and on-line estimation of it.
Method detects confounders in high-dimensional linear models using spectral measure first moments.
problem Detecting confounders in high-dimensional linear models.
method Uses the first moment of the spectral measure of the regression coefficient vector.
result Statistical asymmetry in first moments of spectral measures indicates the presence of confounders.
Detects graph topology changes from noisy signals using prior spectral information.
problem Detecting changes in graph topology from graph signals.
method Leverages graph filtering and subspace detection to distill problem into a CUSUM-based algorithm.
result Demonstrates the effectiveness of incorporating prior spectral signatures for change-point detection.
Khovanov homology detects trefoil knots.
problem Identifying knots using homology.
method Spectral sequence to knot Floer homology.
result Reduced 2-coloured Khovanov homology detects trefoil.
Novel method detects changes in noisy dynamic networks.
problem Change detection in noisy dynamic networks with sparsity and degree heterogeneity.
method Adapted Procrustes analysis to embedded points for vertices in spectral embedding.
result CDP successfully detects various types of vertex-based changes.
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.
Detects figure-eight knot using Khovanov homology.
problem Detecting the figure-eight knot.
method Using Dowlin's spectral sequence from Khovanov homology to knot Floer homology.
result Reduced Khovanov homology (over Q) detects the figure-eight knot.
New spectral clustering method improves community detection in sparse networks.
problem Community detection in sparse networks using spectral clustering.
method Data-driven regularization and novel spectral truncation for adjacency matrix.
result Consistency results for community detection in general SBM and beyond.
Proposes a new spectral embedding norm for better cluster separation in unbalanced datasets.
problem Challenges traditional spectral clustering in unbalanced datasets, especially in anomaly detection.
method Introduces the spectral embedding norm, summing the squared values of the first I normalized eigenvectors. result Demonstrates improved performance in separating clusters from background in various datasets.
A fast spectral algorithm detects community structure in evolving graphs.
problem Detecting community structure in time-evolving sparse graphs.
method Extension of the Bethe-Hessian matrix for spectral community detection.
result The algorithm reaches the optimal detectability threshold and outperforms other methods.
Detects anomalies in forest Ladar data using spectral and temporal signatures.
problem Anomaly detection in cluttered scenes using Ladar data.
method Learned subspace and coefficients for co-occurring local-patterns, modified optimization scheme for subspace learning.
result Detects spectral and temporal anomalies in FW-MSL data, supports tree species classification.
New math detects unlinks using HOMFLYPT homology.
problem Detecting unlinks in knot theory.
method Applied Rasmussen spectral sequence to HOMFLYPT homology over Z2. result HOMFLYPT homology over Z2 detects unlinks. Spectral method detects communities in sparse hypergraphs, achieving detection threshold.
problem Community detection in sparse hypergraphs.
method Non-backtracking operator and spectral approach.
result Spectral method achieves detection threshold for sparse HSBMs.
Graph signal processing detects hallucinations in large language models.
problem Detecting factual reasoning from hallucinations in large language models.
method Modeling transformer layers as dynamic graphs, using spectral analysis to define diagnostics.
result Spectral signatures can distinguish different types of hallucinations and achieve high accuracy.
Spectral method for joint community detection and group synchronization.
problem Jointly detecting communities and synchronizing orthogonal groups in graphs.
method Spectral decomposition followed by CPQR factorization.
result Near-optimal guarantees for exact and stable recovery of cluster memberships and orthogonal transforms.
Two spectral clustering methods for multi-layer networks are analyzed and compared.
problem Community detection in multi-layer networks.
method Sum and debiased sum of squared adjacency matrices for spectral clustering.
result Debiased sum of squared adjacency matrices outperforms sum of adjacency matrices.
New method detects global structures in sparse or noisy data.
problem Localization of eigenvectors in sparse or noisy data.
method Learn a regularization matrix from localized eigenvectors.
result Suppresses eigenvalues associated with localized eigenvectors.
New spectral clustering method for graphs with uneven node degrees.
problem Challenges in community detection for graphs with heterogeneous degree distributions.
method Spectral clustering on spherical coordinates with degree correction.
result Improved performance in representing computer networks.
New invariants detect a specific graph in spatial webs.
problem Detecting specific graphs in spatial webs.
method Introduced new invariants and used spectral sequences.
result Proved invariants detect the planar theta graph.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
Prime homology detects split links in prime characteristic.
problem Detecting split links in prime characteristic.
method Uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients.
result Reduced sl(P) link homology detects split links in Z/P. The paper detects changes in graph signal means offline.
problem Segmenting and detecting changes in multivariate signals over graph nodes.
method Model selection approach exploiting sparsity in spectral domain.
result Proof of non-asymptotic oracle inequality for change-point detection.
New outlier detection method using graph Laplacian spectrum boosts performance.
problem Detecting outliers in large datasets efficiently.
method Boosted outlier detection based on graph Laplacian spectrum.
result Outperforms existing methods on synthetic datasets.
Study instanton Floer homology for links in RP^3 and use it to detect knots.
problem Detecting knots in RP3 using instanton Floer homology. method Compute instanton Floer homology for links in RP3 and use spectral sequences. result Khovanov homology detects the unknot and projective unknot in RP3. Spectral algorithms solve optimal community detection and related problems.
problem Optimal detection of community structures and related substructures.
method Spectral algorithms applied to various planted substructures.
result Spectral algorithms achieve optimal performance for a wide range of planted substructures.
Unified framework improves spectral graph clustering with generative community models.
problem Combining model-based and model-free approaches for robust community detection.
method SGC-GEN: Combines SGC with GENerative community models for theoretical and practical improvements.
result SGC-GEN provides theoretical guarantees and superior performance in community detection.
Paper studies community detection in censored hypergraphs using information theory.
problem Community detection in censored hypergraphs with missing values.
method Information-theoretic approach, polynomial-time algorithm, spectral algorithm with refinement.
result Derives information-theoretic threshold for exact recovery of community structure.
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.
Detects anomalies in noisy data from linear systems.
problem Identifying samples of noise in a linear dynamical system.
method Robust spectral filtering and anomaly detection method.
result Guaranteed statistical performance in identifying noise samples.
Improved community detection in sparse graphs using Bethe-Hessian matrix.
problem Community detection in sparse heterogeneous graphs.
method Spectral clustering based on the Bethe-Hessian matrix Hr for degree-corrected stochastic block models. result Clustering is insensitive to degree heterogeneity for r=ζ. MethaneMapper detects methane emissions with high accuracy and reduced model size.
problem Challenges in detecting and quantifying methane emissions from AVIRIS-NG data.
method Spectral absorption wavelength aware transformer network, introducing two novel modules.
result Achieves 0.63 mAP in detection and reduces model size by 5x.
New graph PCA and dictionary learning methods detect cyber intrusions.
problem Detecting anomalous connectivity patterns in graphs.
method Multi-centrality graph PCA and dictionary learning.
result Effective detection of anomalous connectivity patterns and attack classification.
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.
Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a…
Solves community detection in sparse hypergraphs above a threshold.
problem Community detection in sparse hypergraphs.
method Generalization of Massoulié's method for sparse random graphs to random hypergraphs.
result Above the threshold, a spectral algorithm constructs a partition correlated with the true partition.
New framework tracks communities in dynamic networks.
problem Discovering and tracking communities in evolving networks.
method Spectral framework on Grassmann manifold for subspace tracking.
result Improved dynamic community detection results across various network types.
SpecAE detects anomalies in attributed networks by projecting them into a tailored space.
problem Detecting anomalies in attributed networks with complex dependencies and nodal attributes.
method Spectral convolution and deconvolution framework, leveraging Laplacian sharpening and density estimation.
result SpecAE effectively detects global and community anomalies in attributed networks.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.
CNN-RNNs detect bird sounds with high accuracy.
problem Automated detection of bird sounds in varied environments.
method Convolutional Recurrent Neural Networks (CNN-RNNs) for feature extraction and dependency capture.
result 88.5% AUC score on unseen data.
New spectral clustering method using LASSO regularization for robust graph partitioning.
problem Lack of theoretical guarantees for spectral clustering on general graph models.
method 1-spectral clustering on a new random model with LASSO regularization.
result Effective and robust to small noise perturbations, validated by simulations and real data.
A test for weak signal detection in noisy data matrices.
problem Detecting a weak signal in a noisy Wigner matrix when the signal-to-noise ratio is small.
method Utilizes linear spectral statistics and hypothesis testing on the data matrix.
result The proposed test is optimal when the noise is Gaussian and can be improved with known noise density.
Detects corruption in agentic models during execution.
problem Inconsistent context, retrieval errors, or adversarial inputs corrupt intermediate steps of reasoning chains.
method Analyzes token graphs induced by attention and computes spectral statistics to emit accept/reject signals.
result A single threshold on the high frequency energy ratio optimally detects context inconsistency in agentic models.
Spectral method for detecting communities in time-varying networks from noisy signals.
problem Detect communities in time-varying networks from noisy signals.
method Spectral algorithm based on latent stochastic blockmodel.
result Consistent recovery of community structure in time-varying networks.
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.
Efficient algorithm for CLSBM reduces misclassification rate.
problem Reducing misclassification in community detection for CLSBM.
method Spectral-based algorithm for CLSBM, with theoretical misclassification bounds.
result Upper bound on misclassification rate of efficient algorithm.