Pith. sign in

REVIEW 4 major objections 6 minor 1 cited by

Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that adding an ℓ0 element-wise sparsity constraint on top of an ℓ2,0 row-sparsity constraint in a PCA-based unsupervised feature selection model yields more discriminative features and better clustering than…

desk verdict The double-sparsity PCA model is new and the experiments are honest, but the global convergence theorem has a load-bearing proof gap and the label-tuned evaluation overclaims significance. read the letter →

arxiv 2501.00726 v1 pith:ZV562JTH submitted 2025-01-01 math.OC cs.LG

Xianchao Xiu , Anning Yang , Chenyi Huang , Xinrong Li , Wanquan Liu This is my paper · ORCID
classification math.OCcs.LG MSC 90C2690C3062H2565K05
keywords unsupervisedfeatureselectionsparseprincipalcomponentanalysisdoublesparsityℓ20normℓ0proximalalternatingminimizationglobalconvergencesimilarityratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that unsupervised feature selection improves when the projection matrix is constrained by two sparsity norms at once: the ℓ2,0-norm, which forces whole rows (features) to zero, and the ℓ0-norm, which forces individual entries to zero. The proposed method, DSCOFS, embeds these constraints in the classical PCA objective and solves the resulting nonconvex problem with a proximal alternating minimization scheme whose subproblems have closed-form solutions or fast solvers. The paper claims this yields better discriminative features than single-sparsity PCA variants, with average clustering accuracy and normalized mutual information gains of at least 3.34% and 3.02% over comparison methods on eight real-world datasets. It also contributes a feature similarity ratio metric and a convergence analysis asserting global convergence to a stationary point.

What carries the argument

The load-bearing object is the penalty problem (7), where the orthogonal constraint is kept on $X$ while auxiliary variables $Y$ and $Z$ carry the two sparsity constraints and are tied to $X$ by quadratic penalties. The $X$-update is solved on a ball constraint using an exact penalty function method (Algorithm 2), and the $Y$- and $Z$-updates are projections onto the entry-sparse and row-sparse sets, implemented by hard thresholding operators. The convergence argument rests on the descent inequality (32) and the KL property of the semi-algebraic objective, which together are claimed to give global convergence to a stationary point.

What would settle it

Take a data matrix $A$ with nonzero covariance and run Algorithm 1 from $X_0=Y_0=Z_0=tI$; along this ray $f = -t^2\operatorname{Tr}(AA^{\top})$, which goes to $-\infty$ as $t$ grows, so the boundedness proof that invokes coercivity cannot hold. One can also check whether the $X$-updates returned by Algorithm 2 satisfy $X^{\top}X \approx I_m$ to the claimed tolerance; if they do not, the exact-minimizer premise of the descent inequality is violated.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that $\|X\|_{2,0}\le r$ and $\|X\|_{0}\le s$ are complementary: row sparsity removes irrelevant and redundant features, while entry sparsity removes irregular local noise, and together they make the selected features more discriminative than either sparsity alone. The paper demonstrates this by adding the two constraints to the PCA model $\min \,-\operatorname{Tr}(X^{\top}AA^{\top}X)$ with $X^{\top}X = I_m$, solving the penalty reformulation by alternating updates, and reporting that DSCOFS is the only method in the comparison that beats the all-features baseline on every real dataset. The theoretical claim is that the iterates globally converge to a stationary point of the penalty problem, with the objective strictly nonincreasing, via the Kurdyka-Lojasiewicz property.

Load-bearing premise

The convergence guarantee assumes the penalty objective is coercive—that $f(X,Y,Z)$ grows to infinity when the variables grow—and that each $X$-subproblem is solved by an exact global minimizer; the empirical gains also assume it is legitimate to tune the number of selected features and sparsity parameters on the true cluster labels.

Editorial extensions

If this is right

  • On all eight real-world datasets tested, DSCOFS achieves the best or second-best ACC and NMI among the compared methods, averaging gains of at least 3.34% in ACC and 3.02% in NMI.
  • On the three synthetic datasets, only DSCOFS selects the two correct original features, suggesting double sparsity recovers relevant features that single-sparsity methods miss.
  • The feature similarity ratio shows that adding $\ell_0$-sparsity changes the selected feature set substantially (e.g., 52% overlap on Isolet), so the improvement is not just a re-ranking of the same features.
  • Statistical tests (Friedman and post-hoc Nemenyi) reject the null hypothesis of equal performance and find DSCOFS significantly different from several single-sparsity baselines.
  • The claimed convergence results imply the alternating scheme is a trustworthy solver for the penalty problem: the objective decreases monotonically and every limit point is stationary.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: If double sparsity is the source of the gain, then on new datasets with noisy high-dimensional features one would expect the optimal element-wise sparsity percentage to be low (around $\alpha=0.1$), because the parameter sensitivity plots show the largest improvements there.
  • Editorial inference: The same row-plus-entry sparsity mechanism could be applied to other unsupervised objectives such as matrix factorization or canonical correlation analysis, since the hard-thresholding updates only require a quadratic least-squares structure.
  • Editorial inference: The feature similarity ratio could serve as a general diagnostic for any two-stage feature-selection method, measuring how much an additional constraint changes the chosen feature set before evaluating downstream accuracy.
  • Editorial inference: The comparison with a deep teacher-student method, while limited to four datasets, suggests the hypothesis that double sparsity captures structure that data-hungry deep selectors miss on small samples; a larger benchmark would test whether the gap persists.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes an unsupervised feature-selection method, DSCOFS, that adds an element-wise ℓ0-norm constraint to the row-sparse ℓ2,0-norm PCA model, giving a double-sparsity constrained problem. The authors reformulate the model with auxiliary variables, solve the subproblems by a proximal alternating minimization scheme (with an exact-penalty inner solver for the orthogonality-constrained X-subproblem and hard-thresholding for Y and Z), and claim a global convergence theorem: the sequence generated by Algorithm 1 monotonically decreases the objective, is bounded, and converges to a stationary point of the penalty problem. Experiments on three synthetic and eight real-world datasets report average ACC and NMI improvements of at least 3.34% and 3.02% over several existing UFS methods, together with an ablation study, statistical tests, and a new feature-similarity metric (FSR).

Significance. If the convergence theorem were correct, it would be a valuable theoretical guarantee for a nonconvex nonsmooth sparsity-constrained PCA model, and the double-sparsity formulation is a natural and potentially useful extension of single-sparsity UFS. The algorithm is computationally attractive because the Y- and Z-subproblems have closed-form hard-thresholding solutions, and the experimental section is extensive: it includes multiple baselines, ablation of the ℓ0 constraint, statistical tests, a stability analysis, and a comparison with a deep UFS method. These are real strengths. However, the advertised global convergence result is the paper's central theoretical contribution, and the proof as written contains load-bearing gaps: the descent inequality assumes an exact global solution that the proposed algorithm does not compute, and the coercivity/bounded-below argument for f is false as stated. Because the headline claim is not established, the theoretical significance of the paper in its current form is much reduced.

major comments (4)
  1. [Section 3.3, Eq. (31) and Algorithm 2] The descent inequality (31) is valid only if X^{k+1} is an exact global minimizer of subproblem (8) and hence is feasible for the orthogonal manifold M. Algorithm 2 does not solve (8): it replaces (8) by the penalty surrogate (11) on the ball B_ρ and generates only approximate iterates via (16)-(19), whose output need not be in M. The equivalence quoted from [35] concerns global minimizers, not the approximate stationary points actually produced by Algorithm 2. Consequently, the monotonicity asserted in Theorem 3.2(a), and everything built on it, is not established by the given proof.
  2. [Section 3.3, Theorem 3.2(b)-(c) and Appendix proof] The proof of Theorem 3.2(b) asserts that f in (24) is coercive and concludes from unboundedness of the sequence that f diverges to +∞. This is false on the stated domain: taking X=Y=Z=tI gives f(X,Y,Z) = -t^2 Tr(AA^T), which tends to -∞ as t→∞ (whenever Tr(AA^T)>0). The proof of (c) also uses the claim that f is bounded below. Although boundedness might be salvageable by restricting to the feasible set M×S×R and using compactness of M together with the growth of the penalty terms, the proof as written does not do this. The boundedness and limit claims are therefore unsupported as stated.
  3. [Section 3.2.1 and Theorem 3.2(d), Eqs. (39)-(50)] The first-order optimality conditions (39) are invoked at X^{k+1} as if it were an exact solution of subproblem (8), but Algorithm 2 provides no such solution. In addition, the passage from a stationary point of the penalty problem (11) to a stationary point of (8) via [35, Theorem 3.1] requires the iterate to be an actual stationary point of (11); Algorithm 2 is run only until a stopping criterion and does not guarantee stationarity of (11), let alone global optimality of (8). Thus the concluding claim that every accumulation point is a stationary point of (7) does not follow from the arguments presented.
  4. [Section 4.1.2 and Tables 2-3] The experimental protocol selects regularization parameters and the number of selected features by grid search using the best ACC/NMI values computed against the true cluster labels. This is a supervised model-selection procedure inside an unsupervised feature-selection pipeline, and it can systematically inflate the reported gains, including the headline average improvements of 3.34% (ACC) and 3.02% (NMI). The comparison should be repeated, or at least supplemented, with a protocol that does not use ground-truth labels for parameter selection, and the current protocol should be disclosed as such.
minor comments (6)
  1. [Section 3.2.1, Algorithm 2] The symbol X^{k+1} is reused both for the inner iterates of Algorithm 2 and for the outer iterate returned to Algorithm 1; this makes the algorithm difficult to follow and should be clarified with a different inner-index notation.
  2. [Section 4.2.2, Table 2] In the COIL20 row, the parentheses around the number of selected features are unbalanced: "100)" should read "(100)".
  3. [Section 4.3.1, Eq. (30)] The symbol n denotes the number of samples in Section 2.1 but denotes the number of selected features in the definition of FSR; a distinct symbol should be used for the feature count.
  4. [Section 3.2, Algorithm 1 input] There is a typo in the algorithm caption: "paraments" should be "parameters".
  5. [Section 3.3, Theorem 3.2(a) and contribution list] The decrease is described as "strictly nonincreasing," but the proof establishes nonincrease; strict decrease would require additional argument that consecutive iterates differ. The wording should be made consistent.
  6. [Section 4.4.3] The empirical convergence curves show that the objective decreases on four datasets, but they do not verify the claimed global convergence to a stationary point; the text should not present these plots as confirmation of Theorem 3.2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; theoretical and empirical claims are not equivalent to their inputs by construction.

full rationale

The paper's empirical claims (ACC/NMI improvements over LapScore, UDFS, SOGFS, RNE, FSPCA, SPCAFS, and SPCA-PSD) are benchmarked against external baselines with shared hyperparameter-search protocols, so they do not reduce by construction to fitted constants. The convergence proof is an internal mathematical argument that invokes external theorems ([35], [36], [39]) with no author overlap with the present paper, and the only self-citation ([33]) is motivational rather than load-bearing. The FSR metric is definitionally a measure of overlap between the method's double-sparse and single-sparse outputs; its use as descriptive evidence of different feature selections is not a circular prediction. Concerns about Theorem 3.2 (inequality (31) requiring exact global minimizers of (8) while Algorithm 2 returns approximate stationary points of the penalized problem (11), and the imprecise coercivity statement in the proof of part (b)) are correctness risks or proof gaps, not circularity, because the claimed result is not obtained by assuming its conclusion or by defining one quantity in terms of another. No specific reduction from output back to input can be exhibited from the text, so the appropriate finding is no significant circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The central method depends on several tuned parameters whose values are not reported, plus an incorrect coercivity assumption in the convergence proof. The main theoretical claims therefore rest on unverified or false premises, while the empirical claims rest on test-label-based parameter selection.

free parameters (5)
  • r (row sparsity level) = varies per dataset, e.g., 100 for Isolet, 40 for warpPIE10P (Table 2)
    Number of nonzero rows kept by the ℓ2,0 constraint; grid-searched over {10,...,100} using true labels.
  • α (element-wise sparsity percentage) = chosen from {0.1,...,0.9} per dataset; values not reported in tables
    Determines s = αdm for the ℓ0 constraint; tuned on true labels.
  • μ1, μ2 (penalty parameters) = not reported
    Weights on the equality penalties X=Y and X=Z in (7); inputs to Algorithm 1, no values given.
  • τ1, τ2, τ3 (proximal parameters) = not reported
    Proximal terms added to guarantee convergence; values not specified.
  • β, ρ, η (exact penalty parameters) = not reported
    β must exceed a theoretical bound that is not checked; ρ chosen greater than sqrt(m); η is a Barzilai-Borwein step.
assumptions (4)
  • ad hoc to paper f(X,Y,Z) is coercive and bounded below
    Invoked in the proof of Theorem 3.2(b); false, since X=Y=Z=tI drives f to -∞.
  • domain assumption The exact penalty function method [35, Thm 3.2] makes (11) equivalent to (8)
    Used in Section 3.2.1; the required β bound is not verified for the chosen parameters.
  • standard math Subproblems (9) and (10) are solved globally by hard thresholding
    Projection onto the ℓ0 and ℓ2,0 balls via truncation is a known result, cited as [38].
  • standard math The KL property holds for the objective with indicator functions of M, S and R
    Used in Theorem 3.2(d); semi-algebraic sets and functions satisfy KL.
invented entities (1)
  • Feature similarity ratio (FSR)
    purpose: Measures overlap between features selected with and without the ℓ0 constraint, as evidence that double sparsity changes the selected set.
    A new metric defined by the authors in (30); it quantifies difference but does not independently verify the advantage of double sparsity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization." pith.science (2026). https://pith.science/paper/ZV562JTH

@misc{pith2026250100726,
  author       = {Pith},
  title        = {Pith review of: Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZV562JTH}},
  note         = {Machine review of arXiv:2501.00726}
}
abstract

Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative feature subsets from the original high-dimensional feature set. In this paper, we propose a new UFS method called DSCOFS via embedding double sparsity constrained optimization into the classical principal component analysis (PCA) framework. Double sparsity refers to using $\ell_{2,0}$-norm and $\ell_0$-norm to simultaneously constrain variables, by adding the sparsity of different types, to achieve the purpose of improving the accuracy of identifying differential features. The core is that $\ell_{2,0}$-norm can remove irrelevant and redundant features, while $\ell_0$-norm can filter out irregular noisy features, thereby complementing $\ell_{2,0}$-norm to improve discrimination. An effective proximal alternating minimization method is proposed to solve the resulting nonconvex nonsmooth model. Theoretically, we rigorously prove that the sequence generated by our method globally converges to a stationary point. Numerical experiments on three synthetic datasets and eight real-world datasets demonstrate the effectiveness, stability, and convergence of the proposed method. In particular, the average clustering accuracy (ACC) and normalized mutual information (NMI) are improved by at least 3.34% and 3.02%, respectively, compared with the state-of-the-art methods. More importantly, two common statistical tests and a new feature similarity metric verify the advantages of double sparsity. All results suggest that our proposed DSCOFS provides a new perspective for feature selection.

Figures

Figures reproduced from arXiv: 2501.00726 by the authors.

Figure 1
Figure 1. The examples of results obtained by different sparsity constraints, where white means the value of the element is 0. single sparsity and actual sparsity. Experimental results show that compared with the state-of-the-art UFS methods, the average clustering accuracy (ACC) and normalized mutual information (NMI) of all datasets are improved at least by at least 3.34% and 3.02%, respectively [PITH_FULL_IMAGE:figures/fu… view at source ↗
Figure 2
Figure 2. The ACC performance of our proposed DSCOFS and other UFS methods, including LapScore, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The flowchart of feature selection and clustering of our proposed DSCOFS, where [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: The original distribution and feature selection results on the synthetic datasets. (a), (f) and (k) [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: The ACC (%) curves of compared methods on eight real-world datasets. All methods select [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]
Figure 6
Figure 6. Figure 6: The NMI (%) curves of compared methods on eight real-world datasets. All methods select features [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]
Figure 7
Figure 7. Figure 7: The sparse visualization of the projection matrix [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]
Figure 8
Figure 8. Figure 8: The post-hoc Nemenyi test results in terms of ACC. [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]
Figure 9
Figure 9. Figure 9: The ACC (%) and NMI (%) with different values of our proposed DSCOFS on four real-world datasets. (a)-(d) are the ACC (%) results; (e)-(h) are the NMI (%) results. LapScoreUDFS SOGFS RNE FSPCA SPCAFS SPCA-PSD DSCOFS 30 40 50 60 70 (a) COIL20 (ACC) LapScoreUDFS SOGFS RN…
Figure 10
Figure 10. Figure 10: The model stability of ACC(%) and NMI(%) of all compared methods on four real-world datasets. [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]
Figure 11
Figure 11. Figure 11: The convergence curves of our proposed DSCOFS on four real-world datasets. [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space

    cs.LG 2026-07 conditional novelty 5.0 of 10

    VPOS greedily selects the feature with the largest weighted PCA loading norm, deflates that direction, and reports the lowest reconstruction MSE on eight benchmarks under a minimum-MSE d-selection rule.

Reference graph

Works this paper leans on

40 extracted references · 39 canonical work pages · cited by 1 Pith paper

  1. [35]

    N. Xiao, X. Liu, Y . Yuan, A class of smooth exact penalty function methods for optimization problems with orthogonality constraints, Optimization Methods and Software 37 (4) (2022) 1205–1241

    work page 2022

  2. [1]

    Y . Fan, J. Liu, J. Tang, P. Liu, Y . Lin, Y . Du, Learning correlation information for multi-label feature selection, Pattern Recognition 145 (2024) 109899

    work page 2024

  3. [2]

    Q. Zhou, Q. Wang, Q. Gao, M. Yang, X. Gao, Unsupervised discriminative fea- ture selection via contrastive graph learning, IEEE Transactions on Image Pro- cessing 33 (2024) 972–986

    work page 2024

  4. [3]

    Huang, Z

    P. Huang, Z. Kong, M. Xie, X. Yang, Robust unsupervised feature selection via data relationship learning, Pattern Recognition 142 (2023) 109676

    work page 2023

  5. [4]

    M. P. Uddin, M. A. Mamun, M. I. Afjal, M. A. Hossain, Information-theoretic feature selection with segmentation-based folded principal component analysis (PCA) for hyperspectral image classification, International Journal of Remote Sensing 42 (1) (2021) 286–321. 31

    work page 2021

  6. [5]

    Z. Liu, Y . Yang, F. Gao, T. Zhou, H. Ma, Deep unsupervised learning for joint an- tenna selection and hybrid beamforming, IEEE Transactions on Communications 70 (3) (2022) 1697–1710

    work page 2022

  7. [6]

    Saberi-Movahed, M

    F. Saberi-Movahed, M. Rostami, K. Berahmand, S. Karami, P. Tiwari, M. Ous- salah, S. S. Band, Dual regularized unsupervised feature selection based on ma- trix factorization and minimum redundancy with application in gene selection, Knowledge-Based Systems 256 (2022) 109884

    work page 2022

  8. [7]

    P. Dhal, C. Azad, A comprehensive survey on feature selection in the various fields of machine learning, Applied Intelligence 52 (4) (2022) 4543–4581

    work page 2022

Show all 40 references
  1. [8]

    G. Li, Z. Yu, K. Yang, M. Lin, C. L. P. Chen, Exploring feature selection with limited labels: A comprehensive survey of semi-supervised and unsupervised ap- proaches, IEEE Transactions on Knowledge and Data Engineering 36 (11) (2024) 6124–6144

    2024

  2. [9]

    X. He, D. Cai, P. Niyogi, Laplacian score for feature selection, Advances in Neu- ral Information Processing Systems 18 (2005)

    2005

  3. [10]

    Y . Yang, H. T. Shen, Z. Ma, Z. Huang, X. Zhou, ℓ2,1-norm regularized discrim- inative feature selection for unsupervised learning, in: IJCAI International Joint Conference on Artificial Intelligence, 2011

    2011

  4. [11]

    F. Nie, W. Zhu, X. Li, Structured graph optimization for unsupervised feature selection, IEEE Transactions on Knowledge and Data Engineering 33 (3) (2021) 1210–1222

    2021

  5. [12]

    Y . Liu, D. Ye, W. Li, H. Wang, Y . Gao, Robust neighborhood embedding for unsupervised feature selection, Knowledge-Based Systems 193 (2020) 105462

    2020

  6. [13]

    H. Zou, T. Hastie, R. Tibshirani, Sparse principal component analysis, Journal of Computational and Graphical Statistics 15 (2) (2006) 265–286

    2006

  7. [14]

    Chang, F

    X. Chang, F. Nie, Y . Yang, C. Zhang, H. Huang, Convex sparse PCA for unsuper- vised feature learning, ACM Transactions on Knowledge Discovery from Data 11 (1) (2016) 1–16. 32

    2016

  8. [15]

    S. Yi, Z. He, X. Jing, Y . Li, Y . Cheung, F. Nie, Adaptive weighted sparse principal component analysis for robust unsupervised feature selection, IEEE Transactions on Neural Networks and Learning Systems 31 (6) (2020) 2153–2163

    2020

  9. [16]

    Z. Li, F. Nie, J. Bian, D. Wu, X. Li, Sparse PCA via ℓ2,p-norm regularization for unsupervised feature selection, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (4) (2023) 5322–5328

    2023

  10. [17]

    Zheng, X

    J. Zheng, X. Zhang, Y . Liu, W. Jiang, K. Huo, L. Liu, Fast sparse PCA via posi- tive semidefinite projection for unsupervised feature selection, arXiv: 2309.06202 (Available: https://arxiv.org/abs/2309.06202)

    arXiv

  11. [18]

    T. Pang, F. Nie, J. Han, X. Li, Efficient feature selection viaℓ2,0-norm constrained sparse regression, IEEE Transactions on Knowledge and Data Engineering 31 (5) (2019) 880–893

    2019

  12. [19]

    J. Wang, H. Wang, F. Nie, X. Li, Sparse feature selection via fast embedding spectral analysis, Pattern Recognition 139 (2023) 109472

    2023

  13. [20]

    H. Chen, F. Nie, R. Wang, X. Li, Fast unsupervised feature selection with bipar- tite graph and ℓ2,0-norm constraint, IEEE Transactions on Knowledge and Data Engineering 35 (5) (2023) 4781–4793

    2023

  14. [21]

    F. Nie, L. Tian, R. Wang, X. Li, Learning feature-sparse principal subspace, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (4) (2023) 4858– 4869

    2023

  15. [22]

    L. Cui, L. Bai, Y . Wang, S. Y . Philip, E. R. Hancock, Fused lasso for feature selection using structural information, Pattern Recognition 119 (2021) 108058

    2021

  16. [23]

    J. Liu, M. Feng, X. Xiu, W. Liu, Towards robust and sparse linear discriminant analysis for image classification, Pattern Recognition 153 (2024) 110512

    2024

  17. [24]

    X. Bian, W. Xu, Y . Wang, Z. Cai, C. Yuen, Joint compressed signal recovery and ris diagnosis via double-sparsity optimization, IEEE Internet of Things Journal 11 (8) (2024) 13327–13339. 33

    2024

  18. [25]

    Zhang, Y

    S. Zhang, Y . Liu, X. Li, Micro-doppler effects removed sparse aperture isar imag- ing via low-rank and double sparsity constrained admm and linearized admm, IEEE Transactions on Image Processing 30 (2021) 4678–4690

    2021

  19. [26]

    S. Zhou, Z. Luo, N. Xiu, G. Y . Li, Computing one-bit compressive sensing via double-sparsity constrained optimization, IEEE Transactions on Signal Process- ing 70 (2022) 1593–1608

    2022

  20. [27]

    Y . Guo, Y . Sun, Z. Wang, F. Nie, F. Wang, Double-structured sparsity guided flex- ible embedding learning for unsupervised feature selection, IEEE Transactions on Neural Networks and Learning Systems 35 (10) (2024) 13354–13367

    2024

  21. [28]

    H. Wang, F. Nie, H. Huang, S. Risacher, C. Ding, A. J. Saykin, L. Shen, Sparse multi-task regression and feature selection to identify brain imaging predictors for memory performance, in: 2011 International Conference on Computer Vision, IEEE, 2011, pp. 557–562

    2011

  22. [29]

    Y . Hu, J. Liu, Y . Gao, J. Shang, DSTPCA: Double-sparse constrained tensor prin- cipal component analysis method for feature selection, IEEE /ACM Transactions on Computational Biology and Bioinformatics 18 (4) (2021) 1481–1491

    2021

  23. [30]

    J. Sun, L. Kong, S. Zhou, Gradient projection Newton algorithm for sparse col- laborative learning using synthetic and real datasets of applications, Journal of Computational and Applied Mathematics 422 (2023) 114872

    2023

  24. [31]

    F. Nie, Q. Chen, W. Yu, X. Li, Row-sparse principal component analysis via coor- dinate descent method, IEEE Transactions on Knowledge and Data Engineering 36 (7) (2024) 3460–3471

    2024

  25. [32]

    Z. Wang, Q. Li, H. Zhao, F. Nie, Simultaneous local clustering and unsupervised feature selection via strong space constraint, Pattern Recognition 142 (2023) 109718

    2023

  26. [33]

    X. Xiu, L. Pan, Y . Yang, W. Liu, Efficient and fast joint sparse constrained canon- ical correlation analysis for fault detection, IEEE Transactions on Neural Net- works and Learning Systems 35 (3) (2024) 4153–4163. 34

    2024

  27. [34]

    S. Chen, S. Ma, L. Xue, H. Zou, An alternating manifold proximal gradient method for sparse principal component analysis and sparse canonical correlation analysis, INFORMS Journal on Optimization 2 (3) (2020) 192–208

    2020

  28. [36]

    B. Gao, X. Liu, X. Chen, Y . Yuan, A new first-order algorithmic framework for optimization problems with orthogonality constraints, SIAM Journal on Opti- mization 28 (1) (2018) 302–332

    2018

  29. [37]

    Huang, Y

    Y . Huang, Y . Dai, X. Liu, Equipping the Barzilai–Borwein method with the two dimensional quadratic termination property, SIAM Journal on Optimization 31 (4) (2021) 3068–3096

    2021

  30. [38]

    Blumensath, M

    T. Blumensath, M. E. Davies, Iterative hard thresholding for compressed sensing, Applied and Computational Harmonic Analysis 27 (3) (2009) 265–274

    2009

  31. [39]

    Bolte, S

    J. Bolte, S. Sabach, M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Mathematical Programming 146 (1) (2014) 459–494

    2014

  32. [40]

    Mirzaei, V

    A. Mirzaei, V . Pourahmadi, M. Soltani, H. Sheikhzadeh, Deep feature selection using a teacher-student network, Neurocomputing 383 (2020) 396–408. 35

    2020

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.