Improved convergence for matrix eigen-decomposition problems.
problem Slow convergence and sub-optimal solutions in matrix eigen-decomposition.
method Deployed variance reduction technique of SGD to Riemannian manifolds.
result Fixed learning rate leads to exponential global convergence rate.
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
problem Lack of sophisticated and nonlinear dimensionality reduction methods.
method Inverse Kernel Decomposition (IKD) based on eigen-decomposition of sample covariance matrix.
result IKD achieves comparable performance to optimization-based methods with faster running speeds.
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
Efficient spectral clustering using autoencoders and landmarks.
problem High computational complexity of spectral clustering.
method Build adjacency matrix using landmarks, define efficient Laplacian matrix, perform eigen decomposition using autoencoder.
result Overall complexity of O(np), where n is data points and p is landmarks. 2L-FUSE enhances feature sparsity through kernel learning.
problem Sparsity and feature selection in regression tasks.
method 2-Layered kernel machines for learning a shape matrix and feature direction identification.
result Minimal yet informative feature sets are identified without losing predictive performance.
Explains eigenvalue and generalized eigenvalue problems with examples.
problem Eigenvalue and generalized eigenvalue problems.
method Introduction and examples from machine learning.
result Solutions to eigenvalue and generalized eigenvalue problems.
Paper analyzes spectral clustering for large graphs using random signals.
problem Complex eigen decomposition for large graphs.
method Graph filtering of random signals for approximate spectral embedding.
result Consistency of spectral clustering in stochastic block model.
Paper proposes an anchor-free topic mining framework for better robustness.
problem Identifying topics without anchor words is challenging.
method Second-order moments, anchor-free approach, one eigen-decomposition, small linear programs.
result Guaranteed topic identification under milder conditions.
Gen-RKM framework generates multi-view data with uncorrelated features.
problem Joint multi-view generation and disentangled feature learning.
method Joint multi-view generation using shared representation; primal and dual formulations; novel training procedure for neural networks.
result Joint multi-view generation and uncorrelated feature learning achieved.
MOSAIC detects change points in dynamic networks with low-rank and sparse changes.
problem Detecting change points in dynamic networks with specific structural properties.
method Eigen-decomposition-based test with screened signals and residual-based adjustment.
result MOSAIC achieves minimax-optimal detection and testing rates.
Paper proposes KIIM to infer causal relationships from data.
problem Inferring causal relationships from data is challenging.
method KIIM captures higher order statistics of conditional distributions.
result KIIM outperforms existing methods in causal inference.
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the …
Eigenvalue and eigenvector estimation improves with asymmetric data.
problem Estimating eigenvalues and eigenvectors from asymmetrically perturbed symmetric matrices.
method Eigenvalue and eigenvector analyses of asymmetrically perturbed low-rank matrices.
result The leading eigenvalue of the data matrix can be significantly more accurate than its singular value.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate …
Eigen-decomposition simplifies quadratic programming with equality constraints.
problem Optimizing solutions under linear equality constraints in quadratic programming.
method Eigenvalue decomposition of the quadratic term matrix to project optimal solutions.
result Established a linear mapping between EQP formulations with and without diagonalized Q. A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance …
Directly approximates functions on unknown data manifolds without complex computations.
problem Function approximation on unknown data-defined manifolds with conservative results from traditional methods.
method Direct approach using graph Laplacian and local approximation techniques without eigen-decomposition or atlas.
result Universal estimates for smooth functions without prior knowledge of the target function.
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training po…
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.
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function κ, provided that the latent positions are i.i.d. from some distribution F. We then consider the exploitation task of vertex classi…
Explains various PCA and SPCA methods with theory and applications.
problem No specific problem stated; focuses on explaining methods.
method Explains PCA, SPCA, kernel PCA, and kernel SPCA methods with theory and applications.
result Comprehensive coverage of PCA and SPCA methods with theory and applications.
ParPIC clusters directed graphs using random walks and diffusion operators.
problem Challenges in vertex-level clustering for directed graphs due to edge directionality.
method Parametrized Power-Iteration Clustering (ParPIC) based on reversible random walks and diffusion operators.
result ParPIC achieves competitive clustering accuracy with improved scalability compared to spectral and teleportation-based methods.
A new method matches moments exactly for large graphs, improving spectral learning.
problem Lack of exact moment matching in spectral density approximations for large graphs.
method Maximum Entropy method for spectral density approximation, with a new algorithm.
result The new method outperforms existing approaches in learning graph spectra.
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.
NCA improves fault detection in nonlinear processes.
problem Fault detection in nonlinear chemical processes.
method Neural Component Analysis (NCA) using feedforward neural networks with orthogonal constraints.
result NCA outperforms traditional PCA and autoencoder methods in fault detection.
One-pass SGD converges in overparametrized neural networks with random data.
problem Understanding convergence of SGD in neural networks with streaming data.
method Overparameterized two-layer neural networks, one-pass SGD, random initialization, NTK eigen-decomposition, VC dimension, McDiarmid's inequality.
result Prediction error converges in expectation under one-pass SGD in overparametrized neural networks.
New method estimates node community memberships in networks.
problem Estimating community memberships of nodes in networks with overlapping communities.
method Sharp eigenvector deviation bounds for Mixed Membership Stochastic Blockmodel (MMSB).
result Uniform rates of convergence for node community membership vectors.
A scalable algorithm for MAX-VAR GCCA with improved performance and structure-promoting regularization.
problem Scalability issues and lack of structural constraints in MAX-VAR GCCA.
method Proposed an alternating optimization (AO) algorithm to handle non-convex MAX-VAR GCCA.
result The algorithm globally converges to a critical point at a sublinear rate and approaches a global optimal solution at a linear rate.
New algorithms extract Koopman invariant subspaces from large-scale data.
problem Difficulty in discerning the Koopman invariant subspace from many Koopman eigenmodes.
method Multi-task feature learning and pruning procedure to remove spurious modes.
result Effective in approximating Koopman operator for complex flows.
New method proves non-contrastive self-supervised learning learns useful features.
problem Understanding how non-contrastive self-supervised learning (NS-SL) learns useful features.
method Proved in a linear network, NS-SL learns a desirable projection matrix and reduces sample complexity. Suggested weight decay acts as an implicit threshold.
result DirectCopy, a simpler and more efficient algorithm, outperforms DirectPred on various datasets.
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.
Transformer-based method discovers objects from images without labels.
problem Discovering objects in images without labeled data.
method Graph-based approach using self-supervised transformer features and normalized graph-cut.
result Significantly boosts performance in unsupervised object discovery.
Radiomics approach improves cardiac CVD diagnosis from cine-MRI.
problem Inaccurate expert visualization or clinical indices for CVD classification.
method Estimating radiomic features from cine-MRI, feature selection, advanced machine learning.
result Radiomics features correctly classified 100 cases of five cardiac classes.
Optimized KECA extracts more expressive features by optimizing kernel decomposition and Gaussian kernel parameter.
problem Improving feature extraction efficiency and robustness in kernel-based data analysis.
method Optimized KECA method using ICA framework with gradient ascent search for optimal feature extraction.
result OKECA produces more expressive features than KECA, and is more robust to kernel parameter selection.
A new metric learning framework for signed graphs using Gershgorin disc alignment.
problem Learning Mahalanobis metrics from signed graphs efficiently.
method Proposes a fast metric learning framework using Gershgorin disc perfect alignment (GDPA) to circumvent full eigen-decomposition.
result Proves that Gershgorin disc left-ends of similarity transform are perfectly aligned at the smallest eigenvalue, enabling efficient optimization.
New method preserves privacy while detecting communities in distributed networks.
problem Privacy-preserving community detection in locally distributed multi-layer networks.
method Privacy-preserving Distributed Spectral Clustering (ppDSC) using randomized response mechanism.
result Developed a novel algorithm that maintains community structure while protecting privacy.
New method clusters high-dimensional data with anisotropic noise.
problem Clustering high-dimensional anisotropic mixtures with varying noise structures.
method Covariance Projected Spectral Clustering (COPO) method that projects data onto a low-dimensional space and reassigns clusters based on estimated covariances.
result COPO achieves minimax-optimal misclustering rates in Gaussian settings.
Global covariance pooling improves deep CNNs' representation and generalization.
problem Capturing richer statistics of deep features for better representation and generalization.
method Integrates global covariance pooling into deep CNNs, addressing challenges with robust covariance estimation and geometry exploitation.
result Proposes MPN-COV Pooling and a Gaussian embedding network, achieving state-of-the-art performance.
Improved neural architecture optimization for energy efficiency.
problem Designing energy-efficient deep learning networks for mobile and edge devices.
method Incorporates energy cost in splitting process and uses a scalable stochastic gradient algorithm to speed up the splitting.
result Trains highly accurate and energy-efficient networks on challenging datasets like ImageNet.
This paper speeds up K-FAC for deep learning by focusing on only a few eigen-modes.
problem Time-consuming computation of Kronecker factors in K-FAC for large layers.
method Theoretical analysis and randomized numerical linear algebra to approximate eigen-spectrum decay.
result Reduces time complexity from cubic to quadratic in layer width, improving efficiency.
New methods estimate mixed memberships in multi-layer networks.
problem Complex community structure in multi-layer networks.
method Spectral methods using eigen-decomposition of aggregate matrices.
result Theoretical guarantees and empirical validation for mixed membership estimation.
Paper tackles small eigen-gap estimation and inference for noisy symmetric matrices.
problem Estimating eigenvectors with small eigen-gap and fine-grained statistical reasoning.
method Eigen-decomposition of asymmetric data matrix, distribution-free procedures, adaptive to heteroscedastic noise.
result Minimax optimal under Gaussian noise, confidence intervals for eigenvalues, small eigen-gap handling.
A new method to compress CNNs without changing architectures.
problem Redundancy in CNN filter weights.
method Replacing filters with a fixed set and a learnable 1D layer.
result Significant reduction in parameters and operations with minimal performance loss.
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
Solves four problems related to circle families in the plane.
problem Four basic problems of circle families in the plane.
method Solves all four basic problems of circle families in the plane.
result All four basic problems are solved.
The paper solves optimal control problems for various convex sets using convex trigonometry.
problem Optimal control problems with 2D convex compact sets.
method Using convex trigonometry to derive extremals for various problems.
result Geodesics in multiple sub-Finsler problems are derived.