Proposes a filtering method for cluster analysis using ℓ0-norm regularization.
problem Improving cluster analysis by filtering data.
method Minimizes a least squares function with a weighted ℓ0-norm penalty, approximated by smooth non-convex functions. result The proposed method can enhance existing clustering techniques.
New method improves signal estimation by convexifying ℓ0-norm constraints.
problem Signal estimation with sparsity and smoothness priors.
method Iterative convex conic quadratic relaxations exploiting ℓ0-norm and smoothness terms. result Significantly better estimators than ℓ1-norm approaches and interpretable parameters. Guarantees recovery of compressible signals from adversarial noise.
problem Recovering compressible signals from noise and adversarial attacks.
method Extends adversarial defense framework to ℓ0, ℓ2, and ℓ∞ norms. result Recovery guarantees for various signal recovery methods under different noise types.
Paper tackles low-rank matrix recovery with column ℓ2,0-norm regularization.
problem Low-rank matrix recovery problems with column sparsity constraints.
method Developed alternating majorization-minimization (AMM) methods with extrapolation and hybrid AMM.
result Global convergence analysis and superior performance in matrix completion problems.
Proposes an efficient method for sparse index tracking with ℓ0-norm constraints.
problem Constructing a sparse portfolio to track a financial index.
method Formulates a new problem using ℓ0-norm constraints, develops an efficient algorithm based on primal-dual splitting. result Demonstrates effectiveness through experiments on S&P500 and Russell3000 datasets.
Proposes a new method for joint sample and feature selection in multi-view data.
problem Cannot detect latent subsets of samples and remove outliers.
method Weighted Sparse Partial Least Squares (ℓ∞/ℓ0-wsPLS) method for joint sample and feature selection. result Developed globally convergent algorithm and iterative algorithms for multi-view data fusion.
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.
New algorithm solves ℓ0-norm constrained multilinear logistic regression for tensor data.
problem Non-convex and nonsmooth ℓ0-norm constraints in multilinear logistic regression. method APALM+ method for globally convergent optimization. result APALM+ ensures convergence to a first-order critical point. Paper tackles low-rank matrix recovery with KL property and DC reformulation.
problem Low-rank matrix recovery with coarse rank estimation.
method Adds ℓ2,0-norm and balanced terms to factorized loss function; establishes KL property and DC reformulations. result Establishes KL property of exponent 1/2 for the composite function and its global minimizers. In this paper, we consider an ℓ0-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is…
Paper analyzes convergence of PAM method for low-rank factorization models.
problem Convergence analysis of PAM method with subspace correction for low-rank factorization models.
method Majorized proximal alternating minimization (PAM) method with subspace correction.
result Established full convergence of PAM method under KL property and column ℓ2,0-norm condition. New method estimates robust mean in high dimensions with minimized outliers.
problem Estimating the mean in high dimensions when a fraction of data is corrupted.
method Formulating the problem as ℓ0-norm minimization under second moment constraints, and using ℓ1 and ℓp minimization techniques. result The proposed method achieves order optimal robust mean estimation and significantly outperforms existing methods.
ALℓ0CORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with ℓ0-norm constraint. result ALℓ0CORE achieves similar results to full Tucker decomposition at a fraction of the cost. This paper uses quantum computing to solve sparse linear regression problems efficiently.
problem Sparse linear regression to identify important features from a large set of variables.
method Formulates the ℓ0 optimization problem as a QUBO problem and solves it using the D-Wave adiabatic quantum computer. result The QUBO solution matches the optimal solution for a wide range of sparsity penalty values across datasets.
The paper tackles tensor factorization and completion from noisy data.
problem Sparse nonnegative tensor factorization and completion from partial and noisy observations.
method Minimizes the sum of maximum likelihood estimation and tensor ℓ0 norm with nonnegativity constraints. result Error bounds and minimax lower bounds are established for the proposed model.
Paper improves ℓ0-SSC for noisy data by proving SDP and proposing Noisy-DR-ℓ0-SSC.
problem Noisy data and less restrictive subspace affinity in sparse subspace clustering.
method Proposes Noisy-DR-ℓ0-SSC, which projects data onto a lower dimensional space and then applies noisy ℓ0-SSC. result Theoretical guarantee on the correctness of noisy ℓ0-SSC in terms of SDP on noisy data. Proposes new ℓ0-based methods for low-rank sparse subspace clustering.
problem Clustering high-dimensional data points represented by low-dimensional subspaces.
method Introduces two ℓ0 quasi-norm based regularizations: GMC-LRSSC and S0/ℓ0-LRSSC. Solves resulting nonconvex optimization problems using alternating direction method of multipliers. result Demonstrates effectiveness of proposed methods on synthetic and real-world datasets.
A new greedy method tackles ℓ0,∞ sparse coding for better image processing.
problem Imbalanced sparsity in ℓ0 and ℓ1 norms for image processing. method Greedy matching pursuit for ℓ0,∞ norm optimization. result Efficient method for ℓ0,∞ sparse coding and dictionary learning. 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.
Paper proposes algorithms for robust 1-bit compressive sensing with nonconvex penalties.
problem Recovering sparse signals from one-bit measurements.
method Develops algorithms based on convex and nonconvex penalties, providing analytical solutions.
result Analytical solutions for several nonconvex penalties are found, making the recovery process faster and more efficient.
New method recovers signals from saturated data using linear loss and nonconvex penalties.
problem Signal recovery from saturated measurements with sign information loss.
method Linear loss and nonconvex penalties (e.g., minimax concave penalty, sorted ℓ1 norm).
result Estimation error is bounded and recovery performance improved.
New algorithm reduces high-dimensional data processing costs and achieves true sparsity.
problem High computational costs and difficulty in achieving true sparsity in distributed inference.
method Two-stage distributed best subset selection with oracle property.
result Correctly finds true sparsity pattern and achieves the oracle property.
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, inpainting, and medical image reconstruction. In this work, we focus in…
The paper proposes a new dictionary learning method for faster and more accurate image classification.
problem Efficient and accurate image classification with compact dictionaries.
method Cross-label suppression and group regularization to learn a discriminative dictionary.
result The proposed method achieves better classification accuracy and computational efficiency compared to existing methods.
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
Unified framework for data poisoning attacks in graph-based semi-supervised learning.
problem Data poisoning attacks on graph-based semi-supervised learning.
method Unified formula for data poisoning attacks, specialized algorithms for regression and classification tasks.
result Data poisoning can be effective even with minimal perturbations.
Proposes a new method for feature selection in non-linear functions.
problem Feature selection for non-linear functions in high-dimensional data.
method Continuous relaxation of Bernoulli distributions to learn feature selection indicators via gradient descent.
result Demonstrates the effectiveness of the approach on synthetic and real-life applications.
A new clustering algorithm REFCMFS improves K-Means efficiency and robustness.
problem Efficiently clustering data with outliers and L0-norm constraints. method REFCMFS uses L2,1-norm robust loss and L0-norm constraint on membership matrix. result REFCMFS achieves more promising performance and efficient optimization.
New method solves graph-structured sparsity problems efficiently.
problem Graph-structured sparsity optimization in complex models.
method Stochastic gradient-based approach for non-convex graph-structured sparsity.
result Linear convergence up to a constant error.
SA-FDR uses simulated annealing for feature selection in high-dimensional data.
problem Feature selection in high-dimensional datasets with high predictive accuracy.
method Simulated Annealing for combinatorial optimisation of feature subsets.
result SA-FDR selects more compact feature subsets with high predictive accuracy.
Analyzes normed modules over metric measure spaces.
problem Understanding the structure of normed modules over metric measure spaces.
method Examines conditions for L0-normed modules to be sections of measurable Banach bundles. result Establishes an equivalence of categories between L0-normed modules and measurable Banach bundles. The paper evaluates deep neural networks' robustness to adversarial perturbations using the L0 norm.
problem Computing the maximal radius of a safe norm ball around an input for a trained DNN without adversarial examples.
method The paper shows the problem is NP-hard and proposes an approximate approach to iteratively compute lower and upper bounds on the network's robustness.
result The approach returns intermediate bounds and robustness estimates that are gradually improved as the computation proceeds.
Optimizes biomarker selection for cost-effective treatment rules.
problem Incorporating multiple biomarkers in treatment selection rules can be costly and reduce model performance.
method Developed procedures for estimating linear and nonlinear combinations of biomarkers using 0-norm penalized weighted classification.
result Demonstrated the importance of feature selection and marker cost in treatment selection rules.
Method introduces topological regularization using information filtering networks.
problem Sparse probabilistic modeling and multicollinear regression.
method Topological regularization via information filtering network.
result Direct application to L0-norm regularized problems. The paper shows how Hamiltonian diffeomorphisms and homeomorphisms can be broken down into smaller, manageable pieces.
problem Fragmenting Hamiltonian diffeomorphisms and homeomorphisms on surfaces.
method Develops a C0-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces, proving it with a Lipschitz estimate. result Hamiltonian diffeomorphisms and homeomorphisms can be decomposed into smaller, compactly supported pieces with a Lipschitz estimate on the C0-norm. Prunes neural networks by setting weights to zero during training.
problem Improving generalization and speeding up neural network training and inference.
method Integrates L0 regularization through stochastic gates and a hard-sigmoid transformation. result Effective in learning sparse neural networks with stochastic gradient descent.
We consider immersions admitting uniform graph representations over the affine tangent space over a ball of fixed radius r>0. We show that for sufficiently small C^0-norm of the graph functions, each graph function is smooth with small C^1-norm.
Proposes sparse QSVM for better generalization and interpretability.
problem Overfitting and difficulty in interpreting full quadratic classifiers.
method Enforces ℓ0-norm constraint to promote sparsity and develops a penalty decomposition algorithm. result The proposed model enhances generalization and produces sparse solutions.
In this note, a gradient estimate for the complex Monge-Ampere equation is established. It differs from previous estimates of Yau, Hanani, Blocki, P. Guan, B. Guan - Q. Li in that it is pointwise, and depends only on the infimum of the solution instead of its C0 norm.
PRAE identifies outliers and reconstructs inliers in autoencoders.
problem Accurately identifying anomalies in data.
method Probabilistic Robust AutoEncoder (PRAE) approach.
result PRAE effectively removes outliers and reconstructs inliers.
Proposes a method for tensor completion with sparse factors and missing data.
problem Recovering nonnegative data from noisy observations with missing values.
method Sparse nonnegative Tucker decomposition with ℓ0 norm for sparsity, maximum likelihood estimation, and error bounds. result The method outperforms existing tensor-based or matrix-based methods in nonnegative tensor data completion.
This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with Kähler metrics ωε when ε→0. Here ωε are flat and have areas ε and ε−1 on the two elliptic curves …
Paper tackles DP-SCO with heavy-tailed data in high dimensions, improving error bounds.
problem Differentially private stochastic optimization with heavy-tailed data in high-dimensional spaces.
method Proposes methods for DP-SCO with polytope constraints and LASSO, analyzing sparsity constraints.
result Achieved near optimal error bounds for DP-SCO with heavy-tailed data.
Robust CG methods avoid data corruption and solve structured statistical estimation problems.
problem Data corruption and heavy-tailed data in structured statistical estimation.
method Robustification of Conditional Gradient (CG) type methods using Huber's corruption model and robust mean gradient estimation.
result Robust CG methods converge linearly with correct sample complexity, even for high-dimensional problems.
Sparse metric repair minimizes changes to data to make distances metric.
problem Repairing noisy metric distances with minimal changes.
method Three combinatorial algorithms to minimize sparsity of changes.
result Guaranteed sparsest solution in one setting, metric repair in others.
Small Nijenhuis tensor found on compact manifolds.
problem Finding compact manifolds with small Nijenhuis tensor.
method Provided explicit examples of manifolds with small Nijenhuis tensor.
result Examples of manifolds with small Nijenhuis tensor in various dimensions.
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called l0 norm. In this paper we develop a Momentumized Iterative Shrinkage Th…
The L^p norm of Poisson brackets is lower semicontinuous on surfaces for p < ∞.
problem Lower semicontinuity of L^p norms of Poisson brackets on surfaces.
method Proof of lower semicontinuity for Cc∞(M) functions on surfaces with dimM=2 and p<∞. result The functional (F,G)↦∥{F,G}∥Lp(M) is lower semicontinuous with respect to the C0-norm on Cc∞(M) when dimM=2 and p<∞.