Unified model for tensor completion using low-rank and sparse Tucker decomposition.
problem Estimating missing data from incomplete tensor measurements.
method Unified low-rank and sparse enhanced Tucker decomposition model with ADMM.
result Our model achieves higher recovery accuracy on various real-world data sets.
Method decomposes streaming data into sparse and low-rank components from compressive measurements.
problem Online decomposing compressive streaming data efficiently.
method Solves n-ℓ1 cluster-weighted minimization to decompose sparse and low-rank components. result Outperforms existing methods for numerical and video data.
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the resid…
3BASiL-TM decomposes LLMs into sparse and low-rank matrices for efficient compression.
problem Efficiently compressing large language models without significant performance loss.
method 3-Block ADMM method and transformer-matching refinement step for sparse plus low-rank decomposition.
result 3BASiL-TM reduces perplexity gap by over 30% and speeds up compression by 2.5x.
Unified framework HASSLE-free decomposes large model weights into sparse and low-rank components.
problem Efficiently compress large foundation models to reduce inference costs.
method Designs a unified framework for sparse plus low-rank matrix decomposition with a local layer-wise reconstruction error objective.
result HASSLE-free framework significantly outperforms state-of-the-art methods in compression and evaluation benchmarks.
New method decomposes corrupted data matrices into sparse and low-rank components.
problem Decomposing corrupted data matrices into sparse and low-rank components.
method Discrete optimization approach with alternating minimization, semidefinite relaxation, and branch-and-bound algorithm.
result High-quality solutions and meaningful bounds for SLR problems.
Proposes a model to relate a tensor feature to a univariate outcome using sparse and low-rank components.
problem Relating a univariate outcome to a feature tensor with sparse and low-rank components.
method Divide-and-conquer strategy, stagewise estimation procedure for unit-rank tensor regression.
result The stagewise solution paths converge to those of regularized regression as step size goes to zero.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems with complexity that scales with the dimension of the data, which…
LSDAT reduces query efficiency for decision-based adversarial attacks.
problem Improving query efficiency for decision-based adversarial attacks.
method Low-rank and sparse decomposition (LSD) to craft perturbations.
result LSDAT achieves superior fooling rates with fewer queries.
New method for factor analysis using nuclear and ℓ0 norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, ℓ0 norm, and KL divergence. Used alternating minimization algorithm. result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish deterministic conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability issue arises with tra…
Paper proposes a method for estimating sparse and low-rank tensors from sketchings.
problem Estimating sparse and low-rank tensors from limited data.
method Two-stage non-convex implementation using sparse tensor decomposition and thresholded gradient descent.
result Exact and stable recovery of tensors in noisy and noiseless cases with high probability.
Proposes a method to learn sparse and low-rank interactions in Ising models with latent variables.
problem Learning sparse interactions in Ising models with latent variables.
method Sparse + low-rank decomposition of Ising model parameters using convex regularized likelihood problem.
result Consistency properties in high-dimensional settings with growing number of variables and samples.
Paper detects communities from graph signals using low-rank excitation modeling.
problem Detect communities in graphs from noisy signals.
method Model signals as graph filter outputs, apply spectral method to covariance matrix.
result Community structure can be retrieved directly from graph signals.
RieCUR improves Robust PCA by combining Riemannian optimization and CUR decompositions.
problem Robust Principal Component Analysis (PCA) to recover low-rank and sparse matrices from their sum.
method Riemannian CUR (RieCUR) algorithm that combines Riemannian optimization and robust CUR decompositions.
result RieCUR achieves state-of-the-art performance in Robust PCA with improved robustness to outliers and comparable computational complexity.
New model encodes multivariate signals more efficiently with sparsity and low-rank constraints.
problem Efficiently encoding multivariate signals with sparsity and low-rank constraints.
method Multivariate convolutional sparse coding with tensor algebra, CP decomposition, and alternating optimization.
result Proves model closely related to Kruskal tensor regression problem with theoretical guarantees.
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
New nonconvex regularizers improve low-rank matrix recovery efficiency and accuracy.
problem Efficiently recover low-rank matrices from incomplete data.
method Factor group-sparse regularization, related to Schatten-p norms.
result Improved generalization error bounds for Schatten-p norms as p decreases.
RKCA combines sparse dictionary learning and robust component analysis for robust low-rank modeling.
problem Learning robust low-rank representations from noisy data.
method Kronecker-decomposable component analysis (RKCA) with efficient learning algorithm.
result RKCA achieves robustness to gross corruption and low-rank modeling.
Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD) algorithm. In contrast to previous sparse principal component analysis (PCA) al…
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …
Robust tensor ring completion improves tensor recovery accuracy and efficiency.
problem Tensor completion sensitivity to sparse components.
method Robust Tensor Ring Completion (RTRC) with weighted nuclear norms and l1 regularization.
result Exact recovery guarantees and superior performance in various tasks.
Improved SVD-based NMF initialization reduces initial error and is faster.
problem Improving NMF initialization to reduce convergence error and computational cost.
method Nonnegative SVD with low-rank correction (NNSVD-LRC) that considers discarded SVD factors.
result Significantly reduces initial error with negligible additional computational cost.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
problem Image matrix recovery under low-rank and smoothness assumptions.
method Projected Robust PCA (PRPCA) framework combining low-rank and smoothness.
result Explicit statistical guarantees for PRPCA, reducing matrix dimensionality.
Paper identifies sparse structures and communities in heterogeneous graphical models.
problem Detecting community structures in graphical models.
method Novel decomposition into sparse and low-rank parts, three-stage estimation procedure.
result Consistent model selection for adaptive ℓ1 penalized estimator. New method for robust PCA with exponential family distributions.
problem Recovering low-rank structure from data matrices with outliers.
method Alternating Direction Method of Multipliers for eextRPCA. result Demonstrated effectiveness in steel sheet defect detection and crime activity monitoring.
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an approximately) low rank matrix Θ⋆ with a second matrix Γ⋆ endowed with a complementary …
The paper proposes a method to estimate tensor regression parameters using low-rank and sparse Tucker decompositions.
problem Estimating tensor regression parameters from limited data.
method Low-rank and sparse Tucker decompositions, non-convex optimization, projected gradient descent.
result The method can linearly converge to an appropriate solution under certain conditions.
New CSC model extracts EEG signals with low noise sensitivity.
problem Analyzing noisy EEG signals during anesthesia.
method Kruskal CSC model using Kruskal decomposition for low-rank tensor activations.
result TC-FISTA efficiently extracts robust, sparse, and interpretable EEG encodings.
Unified analysis for robust PCA decomposition with sparse components in known dictionaries.
problem Robust PCA decomposition with sparse components in known dictionaries.
method Convex demixing method for undercomplete and overcomplete dictionary cases.
result Successful recovery of constituent components up to a certain global sparsity level.
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.
Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.
problem High-dimensional time series forecasting with over-parameterization issue.
method Sparse Tucker decomposition and graph regularization for tensor-based model.
result Non-asymptotic error bound and superior performance in numerical experiments.
A novel algorithm converges for solving a specific matrix decomposition problem.
problem Nonlinear matrix decomposition with ReLU function for sparse data.
method Introduced a reparametrization of the Latent-RMD model and developed eBCD for convergence proof.
result eBCD converges and outperforms state-of-the-art methods on various data sets.
New algorithms improve RPCA for large matrices with upper rank bounds.
problem Efficiently decompose large matrices into low-rank and sparse parts.
method Combine regularization and matrix multiplication approaches with upper rank bounds.
result Proposed algorithms are faster and more robust than existing methods.
This paper covers robust subspace learning and tracking methods.
problem Learning and tracking subspaces in the presence of outliers.
method Robust PCA, Robust Subspace Tracking, Robust Subspace Recovery.
result Effective methods for handling outliers in subspace learning and tracking.
New algorithm separates vocals from music recordings efficiently.
problem Separate vocal and instrumental parts in music recordings.
method Informed group-sparse representation for linear-time singing voice separation.
result Efficacy confirmed on iKala dataset; music accompaniment follows group-sparse structure.
Proposes a convex model for mixed logit to handle individual heterogeneity.
problem Non-convex optimization in mixed logit models for individual heterogeneity.
method Sparse and low-rank decomposition for convex formulation.
result Convex formulation avoids simulation-based approximation and unstable model interpretation.
Algorithm learns a better sketch matrix for low-rank approximations.
problem Efficiently compute low-rank approximations of large matrices.
method Uses a learned sketch matrix instead of random matrix for optimization.
result Learned sketch matrix reduces approximation loss significantly compared to random matrix.
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the collection. Recently, "self expression", the idea of using a small subset of data vect…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
We solve robust regression and matrix completion problems with sparse and low-rank models.
problem Adversarial contamination and noisy matrix completion in high-dimensional settings.
method Subgaussian statistical learning framework, trace-regression with matrix decomposition, novel Huber-type loss.
result Near-optimal estimation rates for robust regression and matrix completion.
New method clusters multi-view data by squeezing hybrid knowledge.
problem Removal of redundant information and fusion of multi-view features.
method Low-rank subspace multi-view clustering with adaptive graph regularization.
result Our method outperforms state-of-the-art algorithms on multi-view benchmarks.
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of O(slogd/T), w…
Bayesian model improves image completion accuracy by automatically learning low rank structure.
problem Improving image completion accuracy with limited data and avoiding overfitting.
method Developed a Bayesian low rank tensor ring model with multiplicative interaction and Student-T distribution for sparse core factors.
result The proposed method outperforms state-of-the-art image completion techniques, especially in recovery accuracy.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
We consider N-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank appr…
AntMan compresses RNNs for faster inference with minimal accuracy loss.
problem Inference performance, cost, and memory requirements of complex RNN models.
method Structured sparsity combined with low-rank decomposition.
result Up to 100x computation reduction with less than 1pt accuracy drop.