方差保持正交选择（VPOS）：主成分分析（PCA）加载空间中通过正交收缩进行贪婪特征选择
Variance-Preserving Orthogonal Selection (VPOS): Greedy Feature Selection via Orthogonal Deflation in PCA Loading Space
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中文总结 AI 辅助
该研究提出无监督特征选择贪婪框架VPOS，在加权PCA加载空间运行，每次选后通过零空间收缩投影方差方向，用可重复规则选超参数d，在八个基准测试中实现低重建MSE且速度快，证明收缩能降MSE。
中文摘要 AI 辅助
我们提出了方差保持正交选择（VPOS），这是一种在加权主成分分析（PCA）加载空间中运行的无监督特征选择贪婪框架。每次选择后，VPOS通过零空间收缩投影出所选特征的方差方向，迫使后续选择覆盖协方差结构的正交部分。每一步都能证明将加载矩阵的秩降低1，且贪婪目标与单调次模最大化相关。通过可重复规则选择单个超参数d：在灵敏度扫描中使重建均方误差（MSE）最小的值。在八个基准测试中，VPOS在所有八个测试中实现了最低的重建MSE，并且在大规模运行时比基于图的方法快10到140倍。在匹配的d下与主成分分析（无收缩）进行比较，证实收缩是主要驱动因素，将MSE降低了10%至73%。
英文摘要
We present Variance-Preserving Orthogonal Selection (VPOS), an unsupervised feature-selection method that performs sequential orthogonal deflation in the variance-weighted principal component analysis (PCA) loading space $\mathbf{V}_d\mathbfΛ_d^{1/2}$. After each feature is selected, its loading direction is projected out of all remaining candidates, so subsequent selections cover complementary directions of the rank-$d$ covariance approximation while returning original variables. We establish rank-reduction guarantees and a determinant-growth interpretation, and distinguish VPOS from greedy selection on raw data, unweighted eigenvector pivoting, Principal Feature Analysis (PFA), and Principal Variable Selection (PVS). Experiments enforce $k\leq d$, tune method-specific parameters on validation observations, and evaluate on unseen outer folds. Across seven labelled benchmarks, VPOS improves held-out normalised reconstruction error over matched PCA without deflation on every dataset, with reductions of 1--78%. It obtains the lowest mean reconstruction error on Wine, Breast Cancer, and MNIST and is within 1.7% of the lowest error on CIFAR-10 and HighDim. On CIFAR-10, VPOS is approximately 24$\times$ faster than the closely related PVS baseline while incurring a 1.7% reconstruction gap. These results establish VPOS as an efficient covariance-coverage method, particularly when correlated high-dimensional data must be represented by a small set of identifiable original variables.
发表机构
- Sabanci University（萨班哲大学）
机构由 AI 辅助整理，请以论文原文为准。
