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.
QAPCA uses quantum annealing for robust PCA.
problem Outliers in data skew L2-norm principal components.
method Quantum annealing for L1-norm optimization.
result QAPCA's reconstruction error is comparable to L1-BF.
Proposes MPCA for robust PCA using mode estimation.
problem Outliers sensitivity in PCA.
method Modal Principal Component Analysis (MPCA) based on mode estimation.
result MPCA shows advantages over conventional methods.
A new method centers outliers in robust PCA without manual intervention.
problem Outliers in robust PCA require manual centering, complicating the analysis.
method Introduces a 'bias trick' to automatically center non-outliers.
result First optimal RPCA algorithm with automatic centering.
Improved data analysis with robust SPCA algorithm.
problem Identifying localized spatial structures and disambiguating time scales in low-rank data.
method Formulated as a value-function optimization problem, then extended with randomized linear algebra methods for scalability.
result Robust and efficient sparse principal components in corrupted data.
Robust PCA reduces to power iterations for outlier-resilient feature extraction.
problem Sensitivity of PCA to non-Gaussian samples and outliers.
method Robust formulation of PCA based on maximum correntropy criterion.
result MCPI reduces to power iterations, making PCA more robust to outliers.
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.
We propose a fair principal component analysis method that balances reconstruction error and subgroup fairness.
problem Fairness and robustness in principal component analysis for consequential domains.
method Distributionally robust optimization over the Stiefel manifold with a Riemannian subgradient descent.
result The proposed method achieves better performance on real-world datasets compared to state-of-the-art baselines.
The paper improves RPCA for separating sparse and manifold components on noisy data.
problem Separating sparse and manifold components from noisy data.
method Nonlinear Robust Principal Component Analysis (RPCA) framework.
result The method successfully separates sparse and manifold components under noisy data.
RKPCA improves robustness of PCA for high-rank matrices.
problem Robust recovery of high-rank matrices corrupted by sparse noises.
method RKPCA decomposes matrices into sparse and low-rank components.
result RKPCA provides high recovery accuracy with theoretical guarantees.
NoL approach improves adversarial robustness by modeling random noise during training.
problem Improving neural network robustness against adversarial attacks.
method Implicit generative modeling of random noise during training.
result Models trained with NoL perform better against a wide range of adversarial attacks.
Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal component methods, namely online moving window robust principal component analysis (OMW…
This work analyzes how frequency components affect CNN predictions and robustness.
problem Lack of frequency-based explanation for CNNs leading to vulnerabilities.
method Frequency component analysis and quantification of their contribution to CNN predictions.
result Adversarial attacks exploit high-frequency features, while robustness comes from low-frequency associations.
IRCUR accelerates RPCA by using CUR decomposition for efficient low rank estimation.
problem Dimension reduction in robust principal component analysis.
method IRCUR employs CUR decomposition to update the low rank component efficiently.
result IRCUR achieves significant computational efficiency compared to existing algorithms.
Paper proposes a new method for exact recovery in robust tensor principal component analysis.
problem Exact recovery of low-rank and sparse components in tensors.
method Proposes a new method based on tensor-tensor product and t-SVD to solve a convex optimization problem.
result Exact recovery achieved in a deterministic fashion without randomness assumptions.
Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Princ…
This paper solves tensor robust principal component analysis via scaled gradient descent.
problem Extracting useful information from tensor data robust to corruptions and ill-conditioning.
method Directly recovers low-rank tensor factors via scaled gradient descent with adaptive thresholding.
result The proposed algorithm converges linearly to the true low-rank tensor at a constant rate independent of the condition number.
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 …
This paper proposes a submodular load clustering method for transmission-level load areas.
problem Traditional load analysis challenges with new electricity usage patterns.
method Robust Principal Component Analysis (R-PCA) and submodular cluster center selection.
result The proposed method efficiently clusters load areas and demonstrates effectiveness in PJM load data.
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three as…
This paper improves PPCA robustness using t-distributions.
problem Improving robustness of probabilistic PCA.
method Using multivariate t-distributions and a hierarchical model. result Clarified the correct correspondence between the multivariate t-PPCA framework and the hierarchical model. New method improves PCA robustness using Wasserstein distances.
problem Uncertainty in probability distribution affects PCA robustness.
method Distributionally robust optimization with Wasserstein distances.
result Explicit reformulation leads to efficient smoothing algorithm.
Advances robust principal component analysis with transformed ℓ1 regularization.
problem Recovering low-rank structures from noisy, partially observed data corrupted by sparse outliers.
method Proposes transformed ℓ1 (TL1) regularization to improve approximations of rank and ℓ0 functional.
result Achieves higher accuracy in estimating low-rank and sparse components compared to classical convex models, especially under non-uniform sampling schemes.
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.
Paper solves TRPCA problem for tensor data with new tensor nuclear norm.
problem Exact recovery of tensor low-rank and sparse components.
method Introduces tensor-tensor product and new tensor nuclear norm to solve TRPCA.
result The new tensor nuclear norm guarantees exact recovery of tensor data.
A new robust PCA estimator combining M-estimators and minimum divergence estimators.
problem Adverse effect of outlying observations in PCA for high-dimensional data.
method Minimum density power divergence estimator combined with a computationally efficient algorithm.
result High breakdown guarantee regardless of data dimension with theoretical support and practical applications.
Robust PCA method works under uncertain covariance.
problem Principal component analysis under uncertain covariance.
method Robust streaming PCA with temporal uncertainty set.
result Noisy power method is rate-optimal in our setting.
Kernel PCA explains self-attention mechanisms in deep learning models.
problem Understanding and explaining self-attention mechanisms in deep learning models.
method Deriving self-attention from kernel principal component analysis (kernel PCA).
result RPC-Attention, a robust attention mechanism, outperforms softmax attention in various tasks.
New method improves tensor completion and robust PCA using non-convex tensor rank and sparsity measures.
problem Challenging tensor rank minimization in machine learning.
method Proposes a non-convex tensor rank surrogate function and sparsity measure, using concavity for optimization.
result Demonstrates improved accuracy and efficiency in tensor completion and robust PCA.
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.
This work solves TRPCA under linear transforms, recovering low-rank and sparse components.
problem Exact recovery of tensor low-rank and sparse components from their sum.
method Convex optimization with weighted tensor nuclear norm and ℓ1-norm.
result The convex program exactly recovers the components under certain incoherence conditions.
UPCA solves data matrix completion with permuted columns.
problem Data matrix completion with permuted columns.
method Algebraic geometry and two-stage algorithm.
result UPCA recovers the ground-truth matrix from corrupted data.
Study validates SV models with jump component and long memory parameter, using robustness and sensitivity analysis.
problem Validation of SV models with jump component and long memory parameter.
method Robustness and sensitivity analysis using bootstrapping and Monte-Carlo filtering on market data.
result Validation of SV models with jump component and long memory parameter.
Paper extends principal component pursuit to hypercomplex numbers for improved audio data analysis.
problem Improving robust principal component analysis for audio data.
method Extends principal component pursuit to polar n-complex and n-bicomplex numbers, deriving proximity operators for ℓ1- and trace-norm regularizers. result Our approach outperforms tensor robust principal component analysis on audio data.
A new non-convex method improves robust PCA with features.
problem Robust Principal Component Analysis with prior feature information.
method A novel non-convex optimization approach for decomposition.
result Exact recovery guarantees with low computational complexity.
Proposes AE for robust PCA, improving robustness to outliers.
problem PCA's sensitivity to outliers.
method Angular Embedding (AE) and Truncated Angular Embedding (TAE).
result AE/TAE outperforms state-of-the-art RPCA methods.
GT-PCA improves PCA for image and time series data.
problem Lack of robustness to transformations in PCA.
method GT-PCA is a neural network that estimates components invariant to specific transformations.
result GT-PCA outperforms alternative methods in synthetic and real data experiments.
We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA with prior information for recursively separating a sequences of frames into spars…
This work shows that a simple local search can recover true principal components in non-negative rank-1 RPCA.
problem Recovering true principal components in non-negative rank-1 robust principal component analysis with noisy measurements.
method Using the Burer-Monteiro approach to cast RPCA as a non-convex and non-smooth ℓ1 optimization problem. result The low-dimensional formulation of symmetric and asymmetric positive rank-1 RPCA has a unique global solution and no spurious local solutions.
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some (arbitrarily) corrupted obse…
Paper proposes a robust method for federated ICA with geometric median aggregation.
problem Federated ICA with permutation ambiguity in client estimations.
method Geometric median aggregation with k-means clustering to resolve permutation ambiguity.
result The method provably remains effective in highly heterogeneous scenarios.
Solves complex machine learning problems with IRW method.
problem Problems with intractable sparsity-inducing norms in machine learning.
method Iteratively Re-Weighted (IRW) method with convergence guarantee.
result IRW method significantly outperforms alternative methods in robust feature selection.
PCR robust to noisy, missing, and mixed-valued covariates.
problem Handling noisy, missing, and mixed-valued covariates in PCR.
method PCR is equivalent to HSVT pre-processing; establishes robustness and finite-sample analysis.
result PCR robust to noise, equivalent to RSC, and can learn good predictive models.
Robust statistics detects anomalies in real data.
problem Anomalies in real data can skew analysis results.
method Robust statistics fits the majority of data and flags outliers.
result Robust methods improve anomaly detection in various data types.
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.
New algorithm rSVDdpd improves robustness and scalability for video surveillance background modeling.
problem Camera tampering and noisy videos make background separation challenging.
method Introduces rSVDdpd, a robust singular value decomposition technique for scalable video surveillance.
result Demonstrates superior performance on benchmark and real-life datasets.
Framework for efficient statistical estimation with privacy guarantees.
problem Statistical estimation problems with differential privacy constraints.
method High-dimensional Propose-Test-Release (HPTR) framework combining exponential mechanism, robust statistics, and resilience.
result Near-optimal utility guarantees and tight local sensitivity bounds for various statistical problems.
Unified analysis for robust PCA with applications to target localization in HS images.
problem Decomposing data matrices into low-rank and sparse components with known dictionaries.
method Unified convex demixing method for entry-wise and column-wise sparse structures, analyzing undercomplete and overcomplete cases.
result Successful recovery of constituent matrices under mild conditions on incoherence, sparsity, and rank.