This paper improves spectral clustering for large datasets using the Nystrom method.
problem Spectral clustering's scalability issues with large datasets.
method A principled spectral clustering algorithm exploiting Nystrom approximation's spectral properties.
result Improved spectral clustering efficiency and accuracy compared to existing methods.
Efficiently scales continuous kernels with sparse Fourier domain learning.
problem High computational and memory demands, spectral bias in continuous kernels.
method Sparse learning in the Fourier domain.
result Efficient scaling of continuous kernels, reduced computational and memory requirements, mitigated spectral bias.
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.
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.
Study spectral learning for odeco tensors, addressing initialization bottlenecks.
problem Recovering orthogonally decomposable tensors under noise.
method Investigates perturbation bounds, non-convex optimization, and initialization strategies.
result Initialization is the main bottleneck for efficient algorithms.
We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…
SpGAT learns graph representations using spectral attention for efficiency.
problem Efficiently capturing global graph patterns with minimal parameters.
method Introduces Spectral Graph Attention Network (SpGAT) using spectral domain attention mechanisms and a fast Chebychev approximation.
result SpGAT achieves better global pattern recognition with fewer parameters compared to GAT.
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
Study uses spectral risk for learning with heavy-tailed data.
problem Learning with heavy-tailed loss distributions.
method Spectral risk with Lipschitz-continuous density, derivative-free learning.
result Excess risk guarantees and improved performance over traditional methods.
FNOs learn solution operators of dissipative equations efficiently via spectral methods.
problem Learning and approximation of solution operators for dissipative equations.
method Introducing spectral methods and deriving FNO approximation bounds and sample complexity guarantees.
result Polynomial sample complexity guarantees for FNOs learning solution operators of dissipative equations.
Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time, we present a highly-scalable spectral approach (GRASPEL) for learning large…
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…
SPEDER extracts state-action abstraction from dynamics for reinforcement learning.
problem Curse of dimensionality and limited applicability of spectral methods.
method Spectral Decomposition Representation (SPEDER) that extracts state-action abstraction from dynamics without policy dependence.
result Theoretical analysis establishes sample efficiency in online and offline settings.
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.
problem Efficiently clustering large networks for trust evaluation.
method Exploits k-core decomposition and motifs to perform motif-based spectral clustering on k-core subgraphs.
result The proposed algorithm is accurate and efficient for large networks.
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 algorithm calculates S-invariants for links efficiently.
problem Cannot be done by standard spectral sequence methods.
method Developed an algorithm for S-invariants of links. result Demonstrated efficiency and applicability to sl(3)-link homology.
A new method speeds up spectral normalization for neural nets.
problem Efficiently controlling the spectral norm of convolutional layers.
method Depthwise separable convolutions with spectral normalization.
result Significant reduction in computational and memory costs.
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…
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and eff…
Spectral clustering improves accuracy and efficiency for clustering discrete distributions.
problem Inaccurate clustering of discrete distributions using traditional methods.
method Spectral clustering combined with distribution affinity measures (MMD, Wasserstein distance) and linear optimal transport.
result Spectral clustering outperforms traditional methods in accuracy and efficiency.
Shampoo achieves higher token efficiency than Muon in language models.
problem Understanding the relationship and relative data efficiency of Shampoo and Muon compared to Adam and Signum.
method Extensive experiments on language models, demonstrating Shampoo's higher efficiency and decomposing its updates.
result Shampoo's benefits are attributed to its application to weight matrices, challenging interpretations based on variance adaptation and whitening.
New method efficiently learns positive-definite curvature for neural nets.
problem Efficiently learn positive-definite curvature for neural net training.
method Spectral-factorized positive-definite curvature learning approach.
result Efficiently applies arbitrary matrix roots and generic curvature learning.
Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the in…
Optimizes data power control in cell-free networks for better spectral efficiency.
problem Maximizing overall spectral efficiency in cell-free networks with multi-objective optimisation.
method Applied scalable multi-objective Bayesian optimisation to solve convergence-time limitations.
result Improved radio resource management in cell-free networks.
PAC-Bayesian matrix completion with a spectral scaled Student prior offers efficient inference.
problem Matrix completion with underlying low-rank structure.
method Spectral scaled Student prior and PAC-Bayesian bounds.
result Minimax-optimal oracle inequality for model misspecification and general sampling distribution.
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
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.
SpecNet2 improves spectral embedding without orthogonalization, achieving better performance and efficiency.
problem Improving spectral embedding methods for better performance and efficiency.
method Optimizes an equivalent objective of the eigen-problem without orthogonalization, allowing separate row and column sampling.
result Local and global convergence of the new objective using batch-based gradient descent is proven, and improved performance and efficiency are demonstrated on simulated and image datasets.
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on C∗-algebra. result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…
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.
A new method for nonstationary Gaussian processes using Fourier features.
problem Efficient simulation of nonstationary Gaussian processes with high-dimensional distributions.
method Discretizes the spectral representation of nonstationary processes, avoiding probability measure assumptions.
result An efficient low-rank approximation of nonstationary spectral densities, consistent and positive semi-definite.
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.
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by…
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To bui…
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
Enhances GPLVM for multi-view data with scalable latent representation learning.
problem Limited kernel expressiveness and computational inefficiency in multi-view GPLVM.
method Introduces a new duality between spectral density and kernel function, uses NG-SM kernel, and applies random Fourier feature approximation for scalability.
result Consistently outperforms state-of-the-art models in learning meaningful latent representations across diverse datasets.
In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convoluti…
New learning-based methods improve spectral efficiency in mmWave full-duplex systems.
problem Residual self-interference and high pathloss in mmWave full-duplex systems.
method Proposed two learning schemes (ELM-HBF and CNN-HBF) using ADMM and MM algorithms for SI cancellation and joint HBF optimization.
result Learning-based schemes achieve at least 22.1% higher spectral efficiency and faster online prediction and training times.
New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed 1-spectral clustering for the unconstrained problem, our method is…
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.