{"id":"267d7b86-2da5-4fc0-9ada-77663f6f64dd","arxiv_id":"2412.16819","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"BSUFS combines ℓ2,p and ℓq penalties in PCA for unsupervised feature selection and reports improved ACC and NMI on benchmark datasets.","lead":"This paper adds a second sparsity penalty to PCA-based unsupervised feature selection, combining row-wise and element-wise sparsity to pick discriminative features. Its bi-sparse method, BSUFS, reports better clustering accuracy on several image and gene datasets than single-sparse PCA baselines.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed advantage over PCA-based UFS baselines is not statistically supported and may be inflated by test-set tuning; the paper's own Nemenyi test finds no significant difference from FSPCA, SPCAFS, SPCA-PSD, or FEN-PCAFS.","rationale":"The reader's weakest assumption concerned the missing sufficient-decrease lemma for Algorithm 1; that is a real theoretical gap and is explicitly admitted in Remark 3.4. However, the paper's primary advertised contribution is empirical: the abstract and conclusion claim consistent improvement and robustness. An algorithm without a convergence guarantee can still be a useful heuristic if the experiments are sound. The experiments, though extensive, are not sound enough to support the central claim: parameters and feature counts are selected on the evaluation data, and the included significance test shows BSUFS is indistinguishable from the strongest PCA baselines. This is a direct contradiction of the claimed advantage, not merely a missing proof. The model formulation and proximal updates are coherent, and the ablation study in Tables IV and V suggests the ℓq term helps on some datasets, so the concern is not that the method is worthless; it is that the paper as written overstates its central finding. A revision that adds proper validation and either produces a significant advantage or weakens the claims would be needed; as submitted, the central claim should not be accepted.","tokens_in":28492,"tokens_out":5400,"duration_ms":49488,"concrete_test":"Run a nested validation study on the eight real-world datasets: split each dataset into tuning and test folds; tune p, q, λ1, λ2, and the number of selected features only on the tuning fold; then evaluate ACC and NMI on the test fold. Compare BSUFS with FEN-PCAFS and SPCA-PSD under the identical protocol using a paired Wilcoxon signed-rank or permutation test across datasets. If the advantage over these PCA-based baselines is not significant after this correction, the central claim that bi-sparse regularization improves unsupervised feature selection is unsupported; if it is significant, the concern is resolved.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim is that BSUFS 'consistently selects discriminative features and performs robustly on different noises,' so the empirical comparison is load-bearing. That comparison fails to establish the claimed advantage over the closest PCA-based baselines. In Section IV-E, Figs. 9 and 10, the post-hoc Nemenyi test shows BSUFS has no statistically significant difference from FSPCA, SPCAFS, SPCA-PSD, or FEN-PCAFS on either ACC or NMI; only the graph-based methods are significantly worse. The raw gaps in Tables II and III (ACC 62.78 vs. 60.56 for FEN-PCAFS; NMI 67.87 vs. 67.39 for SPCA-PSD) are within the noise of that comparison. In addition, Section IV-A.2 selects regularization parameters from a candidate set, and Tables II and III report 'the best result with the number of features shown in brackets,' meaning the number of selected features is chosen to maximize ACC on the same data used for evaluation. No separate validation split is described. This selection-on-test-set protocol can inflate BSUFS's apparent advantage and undermines the 'consistently selects' wording. Because the paper's own statistical analysis contradicts the headline empirical claim, the central benefit of the bi-sparse model is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes BSUFS, an unsupervised feature selection method built from PCA with two nonconvex sparsity regularizers: an ℓ_{2,p} row-sparsity term for feature selection and an ℓ_q elementwise sparsity term for noise suppression, with p,q ∈ [0,1). The model in problem (8) unifies SPCAFS and the Lagrangian form of FSPCA as special cases. The algorithm is a proximal alternating minimization scheme (Algorithm 1) in which the W-subproblem is solved by trust-region Riemannian optimization and the U and V subproblems by closed-form proximal operators. The paper reports synthetic and real-world clustering experiments, ablation studies, statistical tests, parameter analyses, and complexity estimates, and it makes code publicly available. The central claims are that BSUFS 'consistently selects discriminative features and performs robustly on different noises' and that the bi-sparse formulation improves over single-sparse PCA-based alternatives.","tokens_in":28742,"tokens_out":4540,"duration_ms":40807,"significance":"If the claimed empirical advantage were established, BSUFS would be a useful contribution: it gives a unified nonconvex bi-sparse PCA framework, includes existing row-sparse PCA methods as special cases, provides closed-form proximal updates for commonly used p and q, and comes with public code and synthetic-data demonstrations of robustness to noise. The ablation and feature-visualization material is also a genuine attempt to attribute the effect to the two regularizers. However, the significance is currently limited because the paper's own statistical analysis does not support the headline advantage over the closest PCA-based baselines, the evaluation protocol appears to select hyperparameters and feature numbers on the test data, and the PAM algorithm lacks a convergence theorem. These are load-bearing issues for the central empirical claim, not presentation defects.","major_comments":[{"comment":"The evaluation protocol appears to fit the model to the test data. Section IV-A.2 selects regularization parameters from a candidate set, and Tables II and III report 'the best result with the number of features shown in brackets,' meaning the number of selected features is chosen to maximize ACC on the same data used for final evaluation. No separate validation split or nested tuning procedure is described. Because the abstract and conclusion claim that BSUFS 'consistently selects discriminative features,' this selection-on-test-set protocol can inflate the reported advantage and should be replaced by a held-out validation protocol or otherwise justified.","section":"Section IV-A.2 and Tables II–III"},{"comment":"The paper's own post-hoc Nemenyi test shows no statistically significant difference between BSUFS and FSPCA, SPCAFS, SPCA-PSD, or FEN-PCAFS on either ACC or NMI; only the graph-based methods are significantly worse. The raw average gaps in Tables II and III (about 2.2 percentage points in ACC and 0.5 percentage points in NMI over the closest baselines) are within the noise of that comparison. Since the central claim of the paper is that BSUFS improves feature selection over existing PCA-based UFS methods, this statistical result directly undermines the headline empirical conclusion as currently worded.","section":"Section IV-E, Figures 9 and 10"},{"comment":"Algorithm 1 is presented as an efficient proximal alternating minimization algorithm, but no convergence theorem is provided. Remark 3.4 states that the sufficient-decrease lemma required by the PAM framework cannot be proved because Algorithm 2 is only guaranteed to converge to a zero Riemannian gradient point, and Section IV-G-4 explicitly says 'the convergence theorem cannot be derived.' The abstract and introduction do not qualify the algorithmic claim accordingly. Either the missing sufficient-decrease argument should be supplied, or the theoretical status of Algorithm 1 should be stated accurately in the main text rather than deferred to future work.","section":"Remark 3.4 and Section IV-G-4"},{"comment":"The text states that 'Case IV consistently achieves the top performance,' but the NMI results do not support this. In Table V, Case IV is worse than Case III on USPS (60.16 vs. 61.14) and umist (67.62 vs. 69.45), and worse than Case II on GLIOMA (45.14 vs. 52.11). Since the added value of the ℓ_q-norm is the core novelty of BSUFS, the ablation evidence needs a more careful quantitative treatment, including the variability across the 50 k-means runs and statistical significance tests, rather than only averages over eight datasets.","section":"Section IV-D, Tables IV and V"}],"minor_comments":[{"comment":"The norms ∥W∥_{2,p} and ∥W∥_q are defined only for p,q ∈ (0,1), but the model (8) allows p,q ∈ [0,1); the p=0 and q=0 cases should be defined precisely (for example via ∥·∥_{2,0} and ∥·∥_0) before they appear in the model.","section":"Section II-A and problem (8)"},{"comment":"The text refers to 'PEN-PCAFS' in the discussion of the Nemenyi test, but the method is FEN-PCAFS; this typo should be corrected.","section":"Section IV-E"},{"comment":"The caption contains the typo 'tranformation matrix' and should read 'transformation matrix.'","section":"Figure 1 caption"},{"comment":"The conclusion says 'respected to ACC and NMI'; this should be 'with respect to ACC and NMI.'","section":"Section V"},{"comment":"The sentence 'Here is another compared method called ALLfea' is awkward; ALLfea is not a feature-selection method but the baseline of using all features, so the description should be reworded for clarity.","section":"Section IV-C"}],"recommendation":"major_revision","confidential_remarks":"The paper has a clear model, reproducible code, and a sensible optimization decomposition, but the empirical claims are currently stronger than the evidence. The most important revisions are to use a proper held-out tuning protocol, to report the comparison against PCA-based baselines together with the non-significance finding, and to either prove or explicitly qualify the convergence statement. If those issues are addressed, the contribution could be acceptable; as it stands, the central practical advantage is not established."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the model is a legitimate extension – combining ℓ2,p row sparsity and ℓq elementwise sparsity in PCA, with p,q in [0,1), which generalizes the p=q=1 model in [31] and SPCAFS. The optimization is standard PAM with proximal operators, and the paper is upfront that no convergence theorem is proved (Remark 3.4). The code is available. That part is fine.\n\nThe soft spot is the empirical claim. The abstract says BSUFS 'consistently selects discriminative features and performs robustly on different noises,' but the Nemenyi test in Figs 9–10 shows no statistically significant difference from FSPCA, SPCAFS, SPCA-PSD, or FEN-PCAFS on either ACC or NMI. The raw average gains (ACC 62.78 vs 60.56, NMI 67.87 vs 67.39) look modest and within noise. Worse, regularization parameters and the number of selected features appear chosen to maximize the evaluation metric on the same test data – no separate validation split is described. That protocol inflates apparent advantages and undercuts the 'consistently' wording. The synthetic experiments do show BSUFS picking the right features on Diamond9, but those are only two toy datasets.\n\nWhere I agree with the authors: the ablation shows Case IV improves over the single-sparse Case III on most datasets, which gives some internal support for the bi-sparse idea. Citing [31] for the p=q=1 special case is correct. The convergence gap is honestly admitted, though it means the algorithm is only empirically convergent.\n\nBottom line: the model is a reasonable incremental contribution, and the paper is honest about its theoretical limitation, but the headline empirical advantage is not statistically established. I would send it to review because the real problems – test-set tuning and overclaiming – are fixable, and the model is defensible. It needs a proper validation split, a more careful statistical claim, and ideally a nonconvex convergence result for the alternating scheme.","headline":"A coherent bi-sparse PCA extension with honest limitations, but the claimed empirical edge over existing PCA-based UFS methods is not backed by the paper's own statistics.","tokens_in":29325,"tokens_out":1799,"would_cite":false,"duration_ms":15831,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C26","90C30","62H25"],"pacs":[],"model":"deepseek-v4-flash","headline":"Adding an elementwise sparsity penalty to row-sparse PCA improves unsupervised feature selection.","keywords":["unsupervised feature selection","bi-sparse optimization","sparse PCA","ℓ2,p-norm","ℓq-norm","proximal alternating minimization","Stiefel manifold","nonconvex optimization"],"falsifier":"Run Algorithm 1 on a small fixed dataset from many random initializations and record the limiting objective values and selected feature sets; if different initializations converge to markedly different objective values or features, the claimed numerical convergence is not robust to initialization. A sharper test is to search for a single iteration in which the full objective increases, which would directly contradict the sufficient-decrease property the missing lemma was meant to provide.","tokens_in":28275,"feed_emoji":"📊","tokens_out":7510,"duration_ms":62742,"temperature":0.7,"pith_summary":"The paper proposes that unsupervised feature selection can be improved by penalizing a PCA transformation matrix both row-wise and element-wise at the same time. Its BSUFS model adds an $\\ell_{2,p}$-norm term, which drives whole rows of the transformation matrix to zero and thereby selects features, and an $\\ell_q$-norm term, which drives individual entries to zero and thereby suppresses noise. With $p$ and $q$ allowed to range over $[0,1)$, the model subsumes earlier single-penalty sparse PCA formulations and the convex double-sparse model as limiting cases. The authors support the proposal with a proximal alternating minimization scheme and experiments on synthetic and eight real-world datasets, where BSUFS reports the best average clustering accuracy and competitive normalized mutual information.","feed_headline":"Two sparsity penalties beat one in unsupervised feature selection","feed_subtitle":"BSUFS pairs row-wise and entrywise shrinkage, lifting clustering accuracy on eight real-world datasets.","key_machinery":"The load-bearing mechanism is a proximal alternating minimization loop whose three subproblems split the two sparsity structures and the orthogonality constraint. The $W$-update is a trust-region problem on the Stiefel manifold using the projected Riemannian gradient and Hessian; the $U$-update applies the proximal map of $|x|^q$ elementwise; and the $V$-update applies the proximal map of $\\|x\\|_p$ row-wise, with closed forms for the tested values $p,q\\in\\{0,1/2,2/3\\}$. Alternating these steps is what lets BSUFS enforce row sparsity and entrywise sparsity simultaneously while keeping $W^\\top W=I_m$.","core_discovery":"The paper's central claim is that a PCA transformation matrix with two simultaneous sparsity structures selects more discriminative features and tolerates noise better than any single-sparsity PCA variant. BSUFS solves $\\min_{W^\\top W=I_m} -\\operatorname{Tr}(W^\\top S W)+\\lambda_1\\|W\\|_{2,p}^p+\\lambda_2\\|W\\|_q^q$ with $p,q\\in[0,1)$, where the $\\ell_{2,p}$ term pushes whole rows of $W$ to zero for feature selection and the $\\ell_q$ term pushes individual entries to zero for noise filtering. In its numerical study the method achieves the highest average clustering accuracy on eight real-world datasets, and ablation experiments indicate that removing either penalty lowers performance.","pith_inferences":["A testable extension: on a dataset whose features are a known union of informative, redundant, and noisy coordinates, the optimal $\\lambda_2$ at fixed $\\lambda_1$ should trace an interior peak in clustering accuracy; the paper's parameter-sensitivity plots hint at this but do not isolate noise type.","Because the paper only proves a zero-gradient result for the $W$ update, the practical convergence of BSUFS is likely initialization-dependent; comparing random and warm starts would quantify how much the reported gains depend on initialization.","The restriction of $p,q$ to $\\{0,1/2,2/3\\}$ is computational, not conceptual; if efficient proximal maps for other values in $[0,1)$ become available, the claimed benefits of the full range could be tested more finely.","The same bi-sparse penalty could be attached to other projection-based objectives, such as tensor PCA or supervised discriminative projections, where the row term would select variables and the entrywise term would denoise."],"forward_implications":["If BSUFS is correct, unsupervised feature selection on high-dimensional unlabeled data can be improved by adding an entrywise sparsity penalty to an already row-sparse PCA model, without changing the feature-scoring procedure.","Because BSUFS reduces to existing single-penalty methods at $\\lambda_2=0$ and to the earlier double-sparse model as $p,q$ approach $1$, a correct BSUFS gives a continuum of models between those baselines, so tuning $p$ and $q$ interpolates between them.","The reported ablation results imply that the $\\ell_{2,p}$ term is the dominant selector while the $\\ell_q$ term is complementary, suggesting that datasets with fine-grained noise benefit most from nonzero $q$.","The sparser transformation matrices shown for BSUFS suggest the method can serve as a label-free preprocessing step for clustering pipelines on image and gene data."],"supporting_citations":[{"why":"Establishes the row-wise $\\ell_{2,p}$ sparse PCA baseline whose objective BSUFS extends with a second sparsity term.","marker":"[24]"},{"why":"Defines feature-sparsity-constrained PCA, the formulation whose Lagrangian relaxation BSUFS recovers when $\\lambda_2=0$.","marker":"[26]"},{"why":"Introduces the double-sparse $\\ell_{2,1}$ plus $\\ell_1$ model that BSUFS reproduces as a limiting case and generalizes to nonconvex $p,q$.","marker":"[31]"},{"why":"Provides the Stiefel manifold trust-region method used to solve the $W$-subproblem inside the alternating scheme.","marker":"[42]"},{"why":"Supplies the proximal operator of $|x|^q$ that solves the $U$-subproblem for the tested values of $q$.","marker":"[43]"},{"why":"Gives the proximal operator of $\\|x\\|_p$ used for the row-wise $V$-subproblem.","marker":"[44]"},{"why":"Defines the proximal alternating minimization convergence framework that the paper invokes and whose sufficient-decrease condition it cannot currently verify.","marker":"[48]"}],"fun_headline_variants":["Two sparsity penalties beat one in PCA feature selection","Bi-sparse PCA selects features and filters noise","Dual sparsity norms improve unsupervised feature selection","Bi-sparse PCA: two penalties for better features"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The convergence argument assumes that each $W$-update decreases the objective by an amount comparable to a sufficiently accurate solution of the Stiefel subproblem, but the trust-region method is only proved to reach a zero Riemannian gradient point, so the paper cannot supply the needed descent lemma and instead presents numerical evidence of decreasing objective values.","fun_headline_variants_meta":{"raw":{"variants":["Two sparsity penalties beat one in PCA feature selection","Bi-sparse PCA selects features and filters noise","Dual sparsity norms improve unsupervised feature selection","Bi-sparse PCA: two penalties for better features"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001192,"raw_usage":{"total_tokens":4916,"prompt_tokens":944,"completion_tokens":3972,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":560,"completion_tokens_details":{"reasoning_tokens":3911}},"tokens_in":560,"tokens_out":3972,"duration_ms":21153,"temperature":1.0,"reasoning_tokens":3911,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:14:59.691961+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1 on a small fixed dataset from many random initializations and record the limiting objective values and selected feature sets; if different initializations converge to markedly different objective values or features, the claimed numerical convergence is not robust to initialization. A sharper test is to search for a single iteration in which the full objective increases, which would directly contradict the sufficient-decrease property the missing lemma was meant to provide.","supporting_citations":[{"cited_title":"Sparse PCA via ℓ2,p-norm regularization for unsupervised feature selection,","cited_arxiv_id":null,"evidence_quote":"Establishes the row-wise $\\ell_{2,p}$ sparse PCA baseline whose objective BSUFS extends with a second sparsity term."},{"cited_title":"Double sparse- representation feature selection algorithm for classification,","cited_arxiv_id":null,"evidence_quote":"Introduces the double-sparse $\\ell_{2,1}$ plus $\\ell_1$ model that BSUFS reproduces as a limiting case and generalizes to nonconvex $p,q$."},{"cited_title":"Beck, First-order Methods in Optimization","cited_arxiv_id":null,"evidence_quote":"Gives the proximal operator of $\\|x\\|_p$ used for the row-wise $V$-subproblem."}],"review_version":1}