This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
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48 results for “Spectral Filtering”
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.
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.
Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.
problem Improving spectral graph convolutional neural networks (graph-CNNs).
method Developed Laplace-Beltrami CNN (LB-CNN) by replacing graph Laplacian with LB operator and approximating spectral filters using Chebyshev, Laguerre, and Hermite polynomials.
result Classification accuracy of LB-CNN is not dependent on the type of polynomials or operators.
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
New equivariant filters improve graph classification.
problem Designing deep learning models for graph symmetries.
method Nonlinear spectral filters (NLSFs) that are equivariant to graph functional shifts.
result NLSFs outperform existing spectral GNNs in graph classification.
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 graph Laplacian matrix to extract its leading eigenvectors, where is the desired number of clusters among objects. This is pro…
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a…
New complexes derived from any filtered cochain complex compute the same cohomology.
problem Constructing cohomologically equivalent subcomplexes from filtered cochain complexes.
method Presenting a general construction that produces subcomplexes from any filtered cochain complex of finite depth.
result The construction of subcomplexes depends only on the filtration up to isomorphism.
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
problem Predicting signals on graph nodes with various structures.
method Spectral kernel learning approach that incorporates a polynomial function in the graph spectral domain.
result The model accurately recovers ground truth spectral filters and outperforms in real-world graph data.
Spectro-Riemannian Graph Neural Networks integrate spectral and curvature signals for better graph representation learning.
problem Enhance graph representation learning by leveraging spectral and curvature signals.
method Proposes Spectro-Riemannian Graph Neural Networks (CUSP) that combines spectral and curvature insights.
result Empirical evaluation shows CUSP outperforms state-of-the-art models by up to 5.3%.
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
problem Handling multi-channel graph signals with limited architectures.
method BankGCN decomposes multi-channel signals into subspaces and uses adapted filters for each subspace.
result BankGCN achieves excellent performance in graph classification on benchmark datasets.
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signals…
We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called feedback-looped filters, to provide better localization on vertices, while still attaining…
Ridge regression linked to Poisson resetting in statistical physics.
problem Understanding and extending ridge regularization in machine learning.
method Connecting stochastic resetting from statistical physics with ridge regularization in machine learning, using renewal processes.
result Exact filter identities for ridge regularization in various reset laws, including exponential and non-exponential.
Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more …
Generative model controls heterophily in graph signals.
problem Controlling heterophily in graph signals for better model effectiveness.
method Combines graphon-based generator with spectral filtering of Gaussian node features.
result Establishes theoretical guarantees for heterophily control and convergence.
SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.
problem Solving ill-posed inverse problems with effective regularization and interpretability.
method SC-Net operates in the spectral domain, learning a pointwise adaptive filter function based on signal-to-noise ratio.
result SC-Net achieves optimal convergence rate and zero-shot super-resolution, matching theoretical bounds.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
problem Extending Fourier cosine method to discrete probability distributions.
method Spectral filters and convergence rates analysis.
result Spectral filters achieve one order faster convergence rates than previously recognized.
RP-GFRFT unifies fractional order and rotation control for graph signals.
problem Lack of rotation-based spectral control in GFRFT and zero-angle degeneracy in AGFT.
method Rotation-parameterized graph fractional Fourier transform (RP-GFRFT) with degeneracy preserving rotation matrix.
result RP-GFRFT improves spectral filtering performance over existing methods.
Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learningcs.LG
Deep learning explained through spectral filtering of hierarchical features.
problem Understanding how deep neural networks learn useful representations from data.
method Neural Low-Degree Filtering (Neural LoFi) as a stylized limit of gradient-based training.
result Predicts how representations are selected layer by layer and explains emergence of concepts.
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.
We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maxi…
State space partitioning based on constrained spectral clustering for block particle filteringstat.ML
A new method for state space partitioning in block particle filtering reduces bias and variance.
problem Overcoming the curse of dimensionality in non-linear, non-Gaussian state space estimation.
method Formulates state space partitioning as a clustering problem and uses spectral clustering with constraints.
result The proposed method effectively groups correlated state variables into smaller blocks, reducing bias and variance.
Study on discrepancy principle for learning algorithms in nonparametric regression.
problem Determining optimal iteration number in nonparametric regression with unknown optimal iteration.
method Investigates discrepancy principle and modified principles for kernelized spectral filters, using deviation inequalities and change-of-norm arguments.
result Classical discrepancy principle is adaptive for slow rates, while modified principles are adaptive for faster rates.
New method controls linear systems with adversarial disturbances.
problem Controlling linear dynamical systems under adversarial conditions.
method Novel convex relaxation using spectral filters from Hankel matrix eigenvectors.
result Polylogarithmic running time improvement over prior methods.
The spectral sequence's -page is a link invariant for .
problem Proving the invariance of the spectral sequence pages.
method Analyzing the spectral sequence construction and its properties.
result The -page is a link invariant for .
Efficient algorithm predicts unknown linear systems with long-term memory.
problem Predicting unknown and partially observed linear dynamical systems with long-term memory.
method Bounding the generalized Kolmogorov width of the Kalman filter model using spectral methods and conducting tight convex relaxation.
result Competes with Kalman filter in hindsight with only logarithmic regret.
GRID invariants block certain Lagrangian cobordisms in 3D.
problem Obstructing decomposable Lagrangian cobordisms in 3D.
method Filtered GRID invariants and link Floer homology.
result GRID invariants obstruct decomposable Lagrangian cobordisms.
FSPA bypasses eigenvalue estimation for quantum PCA, achieving optimal complexity and robustness.
problem Quantum PCA eigenvalue estimation is computationally expensive and prone to errors.
method Filtered Spectral Projection Algorithm (FSPA) that projects onto the dominant spectral subspace directly.
result FSPA achieves optimal complexity and robustness, outperforming classical methods.
Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distancephysics.data-an
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a mu…
New method controls linear systems with partial info and disturbances.
problem Controlling linear dynamical systems under partial observation and adversarial disturbances.
method Double Spectral Control (DSC) using two-level spectral approximation strategy.
result Matches best known regret guarantees with exponential runtime improvement.
GWCA analyzes cross-graph correlations for movie retrieval.
problem Cross heterogeneous graph comparison in movie retrieval.
method Spectral graph filtering, Wasserstein metric learning, generalized eigenvalue decomposition.
result Surprise consistency in learning processes and closed-form solution.
Proposes a new graph trend filtering model for inhomogeneous graph signals.
problem Estimating piecewise smooth signals over a graph with varying smoothness levels.
method Introduces a l2,0 norm penalized Graph Trend Filtering (GTF) model and two solution methods: spectral decomposition and simulated annealing.
result The GTF model performs better than existing approaches in denoising, support recovery, and semi-supervised classification.
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
In deep neural networks, the spectral norm of the Jacobian of a layer bounds the factor by which the norm of a signal changes during forward/backward propagation. Spectral norm regularizations have been shown to improve generalization, robustness and optimization of deep learning methods. Existing methods to compute th…
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clusterin…
Floer homology of families Imath.SG
In principle, Floer theory can be extended to define homotopy invariants of families of equivalent objects (e.g. Hamiltonian isotopic symplectomorphisms, 3-manifolds, Legendrian knots, etc.) parametrized by a smooth manifold B. The invariant of a family consists of a filtered chain homotopy type, which gives rise to a …
We introduce the notion of a Khovanov-Floer theory. Roughly, such a theory assigns a filtered chain complex over Z/2 to a link diagram such that (1) the E_2 page of the resulting spectral sequence is naturally isomorphic to the Khovanov homology of the link; (2) this filtered complex behaves nicely under planar isotopy…
We investigate Bar-Natan's characteristic two Khovanov link homology theory studying both the filtered and bi-graded theories. The filtered theory is computed explicitly and the bi-graded theory analysed by setting up a family of spectral sequences. The E_2-pages can be described in terms of groups arising from the act…
In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation o…
Adaptive spectral RL method enhances RL performance and interpretability.
problem Balancing interpretability and performance in reinforcement learning.
method Spectral based linear RL approach with adaptive regularization.
result Near-optimal bounds for parameter estimation and generalization error.
We propose the product-of-filters (PoF) model, a generative model that decomposes audio spectra as sparse linear combinations of "filters" in the log-spectral domain. PoF makes similar assumptions to those used in the classic homomorphic filtering approach to signal processing, but replaces hand-designed decompositions…
Kullback-Leibler distance as a measure of the information filtered from multivariate dataphysics.data-an
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation …
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
The Khovanov homology of a link in and the Heegaard Floer homology of its branched double cover are related through a spectral sequence constructed by Ozsváth and Szabó. This spectral sequence has topological applications but is difficult to compute. We build an isomorphic spectral sequence whose underlying filte…
Defending Collaborative Filtering Recommenders via Adversarial Robustness Based Edge Reweightingcs.LG
Defense against user shilling attacks in collaborative filtering using edge reweighting.
problem Vulnerability of collaborative filtering to profile injection attacks.
method Adversarial robustness based edge reweighting to attenuate non-robust edges.
result Effective defense against various types of attacks demonstrated through experiments.