Optimizes graph spectral density learning for large networks.
problem Ad-hoc kernel function and bandwidth selection in graph spectral techniques.
method Maximum Entropy approach to learn a smooth graph spectral density.
result Outperforms comparable iterative spectral approaches on synthetic and real graphs.
This study bridges the gap between spatial and spectral GNNs.
problem Lack of direct comparison and cross-reference of existing GNNs.
method Systematically categorizes and examines GNNs into spatial and spectral domains.
result Establishes a strong relationship between spatial and spectral GNNs.
Unified theory simplifies spectral graph analysis.
problem Simplifying spectral graph analysis techniques.
method Recast spectral graph analysis as nonparametric function estimation.
result Unified formalism and algorithm for spectral graph techniques.
Regularization improves spectral embedding by focusing on the largest blocks.
problem Improving the quality of spectral embedding for graph data.
method Explained the impact of complete graph regularization on spectral embedding of a block model.
result Regularization forces spectral embedding to focus on the largest blocks, making it less sensitive to noise or outliers.
Improved spectral clustering algorithm for better performance.
problem Improving the performance of spectral clustering algorithms.
method Developed a new performance guarantee under a weaker assumption and evaluated using a different spectral embedding map.
result Better performance guarantee under a weaker assumption and evaluation of a new spectral embedding map.
Graph pooling method uses GNN to cluster graphs efficiently.
problem Efficiently cluster graphs for graph pooling.
method Formulates a continuous relaxation of minCUT, trains GNN to minimize it.
result GNN-based clustering learns fast and performs well.
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.
problem Understanding when graph convolutional networks fail compared to spectral embedding.
method Presented a simple generative model to illustrate failure.
result Graph convolutional networks fail to use eigenvectors beyond the first in certain graphs.
CNNs adapted for graph data with fast localized spectral filters.
problem Generalizing CNNs to irregular domains like graphs.
method Spectral graph theory for efficient localized convolutional filters.
result Efficient deep learning system for graph data with linear complexity.
The paper analyzes the Spectral Method for clustering data points on Union of Subspaces.
problem Clustering data points on Union of Subspaces.
method Constructing a Random Geometry Graph (Subspace Clustering) and analyzing it using spectral methods.
result Established a theory to analyze the Spectral Method's efficiency on Union of Subspaces.
A new method boosts graph neural networks by preventing over-smoothing and over-squashing.
problem Graph Neural Networks struggle with long-range signals and over-smoothing/over-squashing.
method Proposes PowerEmbed, a layer-wise normalization technique inspired by spectral graph embedding.
result PowerEmbed prevents over-smoothing and avoids over-squashing, improving performance on heterophilous graphs.
New spectral clustering for directed graphs reveals socio-economic patterns.
problem Spectral clustering for directed graphs is unsatisfactory due to edge directionality.
method Proposes a complex-valued matrix representation and analysis for directed graphs.
result Our approach reveals socio-economic patterns in internal migration data.
Develops mixed quantization for graph vector bundles.
problem Solving asymptotic spectral problems on graph vector bundles.
method Mixed quantization technique for graph vector bundles.
result Applications to various spectral problems.
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.
Developed a framework for designing filters in spectral GCNNs with improved performance.
problem Designing effective filters for spectral GCNNs with regularization properties.
method Exploring regularization properties of graph Laplacian and proposing a generalized framework for filter design.
result New filters derived from the framework outperform state-of-the-art techniques in semi-supervised node classification.
Graph Laplacians and machine learning predict properties of finite graphs.
problem Understanding properties of finite graphs using spectral and topological methods.
method Combining graph Laplacians, spectral inequalities, machine learning, and topological data analysis.
result Neural networks can accurately predict graph properties like Ricci-flatness and spectral gaps.
This paper provides theoretical guarantees for spectral clustering using graph cuts.
problem Lack of performance guarantees for spectral clustering.
method Convex relaxation of graph cuts, spectral proximity condition, algebraic connectivity, inter-cluster connectivity.
result Deterministic bounds for successful spectral clustering are derived.
A faster method for spectral clustering using graph signal processing.
problem High computational cost in spectral clustering for large datasets.
method Graph filtering and random sampling of bandlimited graph signals to approximate spectral clustering.
result The method significantly reduces computation time while maintaining clustering accuracy.
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
problem Challenges in 3D shape analysis and registration, especially with large variability.
method Combining spectral graph matching with Laplacian embedding for large graphs, using commute-time embedding and PCA.
result A method to register shapes with different samplings and isometric deformations.
Proposes robust local scaling using conditional quantiles of graph similarities.
problem Spectral analysis sensitivity to parameters and noise.
method Auto-encoding neural network for inferring conditional quantiles of similarity functions.
result Proposed approach outperforms existing methods in spectral clustering and single-example label propagation.
We propose a fast algorithm for spectral embedding using stochastic gradient descent.
problem Scalability issue in spectral embedding due to eigendecomposition bottleneck.
method Reformulate spectral embedding as a stochastic optimization problem, replacing orthogonality constraint with an orthogonalization matrix.
result Efficient algorithm based on mini-batch gradient descent that outperforms existing techniques in execution speed.
New method clusters evolving networks using spatio-temporal graph Laplacian.
problem Clustering communities in time-varying graphs.
method Extends spectral clustering to dynamic graphs using CCA and spatio-temporal graph Laplacian.
result The spatio-temporal graph Laplacian clearly interprets cluster evolution over time.
Graphon pooling preserves spectral properties in GNNs, reducing overfitting.
problem Unclear pooling and sampling strategies in GNNs that alter graph structure.
method Modeling graph layers as elements of a sequence converging to a graphon.
result Graphon pooling GNNs reduce overfitting and improve performance.
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, ε-graphs and k-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…
Binary embeddings speed up graph data retrieval.
problem Efficiently retrieving graphical data.
method Binary valued embeddings modeled as coin flips with varying bias, optimized using continuous optimization techniques.
result Binary embeddings outperform other methods on various datasets.
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.
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.
Paper optimizes Laplacian regularization for sparse network clustering.
problem Improving spectral clustering in sparse networks.
method Formally determines optimal Laplacian regularization.
result Proper regularization is closely tied to state-of-the-art techniques.
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks and for visualisation purposes. Whereas a large number of dedicated…
The paper proves limit theorems for graph embeddings out-of-sample.
problem Proving limit theorems for graph embeddings out-of-sample.
method Least-squares and maximum-likelihood objectives for adjacency and Laplacian spectral embeddings.
result Out-of-sample extensions based on these objectives obey central limit theorems and concentration inequalities.
Characterizes lamination spaces of graphs on a pair of pants.
problem Understanding lamination spaces of graphs on a pair of pants.
method Identifying lamination spaces as lattice polytopes and using graph exploration technique.
result Characterizes the polytopes that arise as lamination spaces of graphs on a pair of pants.
This paper analyzes various graph clustering methods and their applications.
problem Dividing graphs into homogeneous groups for diverse applications.
method Traditional and deep learning-based clustering methods are compared.
result Deep learning techniques improve clustering accuracy.
TM-GCN learns dynamic graph embeddings using tensor algebra.
problem Handling dynamic graphs in graph neural networks.
method Tensor M-product for dynamic graph convolution.
result TM-GCN outperforms existing methods on edge classification and link prediction.
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several emp…
Bayesian model estimates latent dimension and communities in graphs.
problem Automatic selection of latent dimension and number of communities in spectral embeddings.
method Bayesian model for simultaneous selection of latent dimension and number of communities.
result Promising performance in recovering latent community structure on simulated and real-world data.
DPSM clusters nodes in data and graph spaces via density propagation and subcluster merging.
problem Automatic clustering of nodes in data and graph spaces.
method Density-based node clustering with propagation process and spectral clustering on subclusters.
result DPSM effectively clusters nodes in both data and graph spaces.
Proposes a parsimonious graph spectral method for time series data.
problem Efficiently transmitting multivariate time series data.
method Graph spectral embedding with unsupervised, parsimonious encoding.
result Near-linear computational complexity and interpretable event structure.
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the detection of a subset of entities whose connectivity is anomalous with respect to the r…
Improved spectral-based GCN for directed graphs.
problem Cannot directly work on directed graphs.
method Redefined Laplacians to improve propagation model.
result Outperforms state-of-the-art methods on directed graph datasets.
The paper explains how regularization improves spectral clustering by reducing sensitivity to noise.
problem Spectral clustering's sensitivity to noise in sparse and stochastic graphs.
method Using graph conductance and regularization to improve spectral clustering.
result Regularization reduces sensitivity to small cuts in the graph, improving clustering accuracy and speed.
Graph reduction preserves spectral and cut properties without significant loss.
problem Can graphs be reduced in size without altering their fundamental properties?
method Restricted spectral approximation, focusing on coarsening.
result Improved quality coarse graphs found without sacrificing speed.
Better spectral partitioning of signed graphs using standard Laplacian.
problem Meaningless partitioning using signed Laplacian eigenvectors.
method Use standard graph Laplacian for spectral partitioning.
result Fiedler vector of standard Laplacian is easier to compute and more beneficial.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
Unified algorithm for latent patterns in SBM and SWM models.
problem Invalid analysis due to misspecified models in graph analysis.
method Combining kernel learning, spectral graph theory, and dimensionality reduction.
result First statistically sound polynomial-time algorithm for latent patterns.
Lecture notes on spectral graph methods at UC Berkeley.
problem No specific problem stated in the abstract.
method Lecture notes based on teaching spectral graph methods.
result No specific key result mentioned in the abstract.
GRASPEL learns large graphs from data efficiently.
problem Learning meaningful graphs from data for various applications.
method Highly scalable spectral approach using graph Laplacians and coarsening techniques.
result Ultra-sparse graphs with improved efficiency and accuracy in spectral clustering and t-SNE.
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.
Estimates spectral density of large implicit matrices efficiently.
problem Estimating eigenvalues of large implicit matrices efficiently.
method Combines randomized estimation techniques to construct unbiased estimators.
result Validated methods on large-scale problems in graph theory and random matrix theory.