Sparse multi-label feature selection via dynamic graph manifold regularization

Zhang, Yao; Ma, Yingcang

doi:10.1007/s13042-022-01679-4

Cited by 21 publications

(10 citation statements)

References 33 publications

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“…Similar to Theorem 2, we can prove that the iteration scheme (28) converges to the unique solution of the regularized SCAD problem of the form…”

Section: Convergencementioning

confidence: 68%

A randomized sparse Kaczmarz solver for sparse signal recovery via minimax‐concave penalty

Niu,

Zheng

2024

Math Methods in App Sciences

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The randomized sparse Kaczmarz (RSK) method is an algorithm used to calculate sparse solutions for the basis pursuit problem. In this paper, we propose an algorithm framework for computing sparse solutions of linear systems, which includes the sparse Kaczmarz and sparse block Kaczmarz algorithms. In order to overcome the limitations of the penalty, we design an effective and new randomized sparse Kaczmarz algorithm (RSK‐MCP) based on the non‐convex minimax‐concave penalty (MCP) in sparse signal reconstruction. Additionally, we prove that the RSK‐MCP algorithm is equivalent to the randomized coordinate descent method for the corresponding dual problem. Based on this result, we demonstrate that the RSK‐MCP algorithm exhibits linear convergence, meaning it converges to a sparse solution of the MCP model when the regularization of MCP is a strongly convex function. Numerical experiments indicate that the RSK‐MCP algorithm outperforms RSK‐L1 in terms of both efficiency and accuracy.

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“…Similar to Theorem 2, we can prove that the iteration scheme (28) converges to the unique solution of the regularized SCAD problem of the form…”

Section: Convergencementioning

confidence: 68%

A randomized sparse Kaczmarz solver for sparse signal recovery via minimax‐concave penalty

Niu,

Zheng

2024

Math Methods in App Sciences

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“…The iterative reweighted algorithms were generalized in [37] to tackle a problem class of the sum of a convex function and a nondecreasing function applied to another convex function. In [14], a general framework of multi-stage convex relaxation was given, which iteratively refines the convex relaxation to achieve better solutions for nonconvex optimization problems. It includes previous approaches including LQA, LLA and the concave-convex procedure (CCCP) [38] as special cases.…”

Section: Methodsmentioning

confidence: 99%

“…To remedy this problem, many nonconvex sparse recovery methods have been employed to better approximate the ℓ 0 -norm and enhance sparsity. They include ℓ p (0 < p < 1) [10][11][12], smoothed L0 (SL0) [13], Capped-L1 [14], transformed ℓ 1 (TL1) [15], smooth clipped absolute deviation (SCAD) [9], minimax concave penalty (MCP) [16], nonconvex shrinkage methods, [17], exponential-type penalty (ETP) [18,19], error function (ERF) method [20], ℓ 1 − ℓ 2 [21,22], ℓ r r − αℓ r 1 (α ∈ [0, 1], r ∈ (0, 1]) [23], ℓ 1 /ℓ 2 [24,25], q-ratio sparsity minimization [26] and smoothed ℓ p -over-ℓ q (SPOQ) [27], among others. For a more comprehensive view, please see the survey on nonconvex regularization [28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Sparse Recovery Based on the Generalized Error Function

Zhou¹

2024

JCM

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In this paper, we offer a new sparse recovery strategy based on the generalized error function. The introduced penalty function involves both the shape and the scale parameters, making it extremely flexible. For both constrained and unconstrained models, the theoretical analysis results in terms of the null space property, the spherical section property and the restricted invertibility factor are established. The practical algorithms via both the iteratively reweighted ℓ1 and the difference of convex functions algorithms are presented. Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances. Its practical application in magnetic resonance imaging (MRI) reconstruction is also investigated.

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“…A key problem is how to choose the regularization function g(•) to improve the reconstruction accuracy and reduce the computational cost. Although the ℓ 2,1 -norm regularization gets its popularity and has been widely used in various applications, it has been shown to be suboptimal in many cases (particularly, it cannot enforce further sparsity when applied to CS) [39][40][41], since the ℓ 0 -norm is a loose approximation of the ℓ 1 -norm and often leads to an over-penalized problem. Consequently, some further improvements are required.…”

Section: Non-convex Optimization For Signal Reconstructionmentioning

confidence: 99%

Compressed sensing of large-scale local field potentials using adaptive sparsity analysis and non-convex optimization

Sun¹,

Zhang²,

Zhang³

et al. 2021

J. Neural Eng.

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Objective. Energy consumption is a critical issue in resource-constrained wireless neural recording applications with limited data bandwidth. Compressed sensing (CS) has emerged as a powerful framework in addressing this issue owing to its highly efficient data compression procedure. In this paper, a CS-based approach termed simultaneous analysis non-convex optimization (SANCO) is proposed for large-scale, multi-channel local field potentials (LFPs) recording. Approach. The SANCO method consists of three parts: (1) the analysis model is adopted to reinforce sparsity of the multi-channel LFPs, therefore overcoming the drawbacks of conventional synthesis models. (2) An optimal continuous order difference matrix is constructed as the analysis operator, enhancing the recovery performance while saving both computational resources and data storage space. (3) A non-convex optimizer that can by efficiently solved with alternating direction method of multipliers is developed for multi-channel LFPs reconstruction. Main results. Experimental results on real datasets reveal that the proposed approach outperforms state-of-the-art CS methods in terms of both recovery quality and computational efficiency. Significance. Energy efficiency of the SANCO make it an ideal candidate for resource-constrained, large scale wireless neural recording. Particularly, the proposed method ensures that the key features of LFPs had little degradation even when data are compressed by 16x, making it very suitable for long term wireless neural recording applications.

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Sparse multi-label feature selection via dynamic graph manifold regularization

Cited by 21 publications

References 33 publications

A randomized sparse Kaczmarz solver for sparse signal recovery via minimax‐concave penalty

A randomized sparse Kaczmarz solver for sparse signal recovery via minimax‐concave penalty

Sparse Recovery Based on the Generalized Error Function

Compressed sensing of large-scale local field potentials using adaptive sparsity analysis and non-convex optimization

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