Learning to Select Features with Manifold Deep Unfolding PCA
Unsupervised feature selection often forces practitioners to hand-tune regularization parameters in sparse PCA models or to collect large labeled datasets for deep learning. This paper proposes MDUFS-Net and MDUFS-Net+, which unfold an ADMM solver for $\ell_{2,0}$-norm regularized PCA into a trainable deep network, embed a Stiefel manifold projection to preserve orthogonality, and optionally add element-wise $\ell_0$ sparsity. The work matters because it tries to retain the interpretability of model-driven optimization while automating parameter adaptation via gradient-based learning.
The proposed methods are methodically constructed and backed by extensive experiments, but the overall contribution is incremental rather than transformative. The deep unfolding architecture is sound and the manifold projection is a sensible addition, yet the empirical claims are undermined by an unfair runtime comparison (CPU MATLAB versus GPU Python) and by asserting that the method avoids the large data requirements of deep learning without providing any low-data experiments. Additionally, the synthetic validation is purely visual, lacking quantitative feature recovery metrics.
The model-driven design is the strongest aspect. Mapping ADMM iterations to network modules (MGradNet, HardNet, Linear) yields a transparent and interpretable architecture, and the QR-based retraction together with the tangent-space projection explicitly maintains the orthogonality constraint $X^{\top}X = I$ throughout unfolding. The ablation studies in Tables IV–VII are thorough: they isolate the contributions of $\ell_{2,0}$ versus $\ell_0$ regularization, manifold projection versus retraction, deep unfolding versus conventional ADMM, and stage-wise versus shared parameters, all showing consistent gains for the full model.
First, the runtime analysis in Section IV-E3 compares MATLAB/CPU baselines against a Python/GPU implementation without any normalization, so the reported efficiency is misleading even though the authors disclose the difference. Second, the abstract states that deep learning methods generally require massive training data, yet MDUFS-Net is itself a deep network trained end-to-end; no experiment demonstrates its advantage in a small-data or few-sample regime. Third, synthetic evaluation relies on selecting the top two features and plotting scatter diagrams rather than computing quantitative selection accuracy such as true positive rate or ranking correlation. Fourth, with $K=15$ unfolding stages and multiple stage-wise learnable parameters ($\lambda_k, \alpha_k, \eta_k, \beta_k, \mu_k$), the model has a large parameter count, but overfitting risks on small datasets like LUNG ($n=203$) are not discussed.
Tables II and III indicate that MDUFS-Net+ achieves the highest average ACC and NMI among the eight compared methods across eight real-world datasets. However, these tables report each method’s best result over varying numbers of selected features (10 to 100), which means the comparison is performed at each method’s own optimal operating point rather than at a fixed feature budget. This protocol is common in UFS literature but should be interpreted cautiously. The superiority over sparse PCA variants such as SPCAFS, FSPCA, and BSUFS is plausible given the adaptive parameter learning, though the evidence would be stronger with direct feature selection fidelity metrics beyond downstream clustering performance.
The authors release code on GitHub, which is a significant positive. Nevertheless, several details needed for exact reproduction are missing or vague: the lower bounds for regularization parameters are set according to feature dimensionality without explicit formulas, initialization strategies for $X^0, Y^0$, and $\Lambda^0$ are not stated, and hardware specifications (GPU model) and batch size are omitted. Most critically, the runtime comparison uses mismatched software and hardware environments, so independent researchers cannot reproduce the timing claims without reimplementing all baselines in the same framework.
Unsupervised feature selection (UFS) is of great significance in image processing and pattern recognition. Nevertheless, existing model-based methods often rely on manually tuned hyperparameters, while deep learning-based methods generally require massive training data. To address these issues, this paper proposes an efficient manifold deep unfolding feature selection network (MDUFS-Net). Technically, we first incorporate the $\ell_{2,0}$-norm into the classic principal component analysis (PCA) framework, then unfold the alternating direction method of multipliers (ADMM)-based iterative algorithm into an end-to-end trainable network, thereby enabling automatic parameter learning. Moreover, a manifold optimization strategy is developed to improve the numerical robustness. On this basis, we further extend MDUFS-Net into an enhanced variant called MDUFS-Net+ by introducing the $\ell_{0}$-norm for more discriminative feature representations. Extensive experiments validate that our proposed MDUFS-Net and MDUFS-Net+ outperform state-of-the-art methods in the UFS task, with promising performance in clustering. Our code is available at https://github.com/xianchaoxiu/MDUFS.
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