With the rapid increase of the data size, it has increasing demands for selecting features by exploiting both labeled and unlabeled data. In this paper, we propose a novel semi-supervised embedded feature selection method. The new method extends the least square regression model by rescaling the regression coefficients in the least square regression with a set of scale factors, which is used for evaluating the importance of features. An iterative algorithm is proposed to optimize the new model. It has been proved that solving the new model is equivalent to solving a sparse model with a flexible and adaptable $\ell _{2,p}$ℓ2,p norm regularization. Moreover, the optimal solution of scale factors provides a theoretical explanation for why we can use $\lbrace \left\Vert \mathbf {w}^{1} \right\Vert _{2},\ldots, \left\Vert \mathbf {w}^{d} \right\Vert _{2}\rbrace${w12,...,wd2} to evaluate the importance of features. Experimental results on eight benchmark data sets show the superior performance of the proposed method.

中文翻译：

---

通过稀疏重缩放线性平方回归进行半监督特征选择

随着数据规模的快速增长，对利用标记数据和未标记数据进行特征选择的需求越来越大。在本文中，我们提出了一种新颖的半监督嵌入特征选择方法。新方法通过使用一组比例因子重新缩放最小二乘回归中的回归系数来扩展最小二乘回归模型，用于评估特征的重要性。提出了一种迭代算法来优化新模型。已经证明，求解新模型等效于求解具有灵活适应性的稀疏模型。$\ell _{2,p}$ℓ2,磷规范正则化。此外，比例因子的最优解为我们为什么可以使用提供了理论解释$\lbrace \left\Vert \mathbf {w}^{1} \right\Vert _{2},\ldots, \left\Vert \mathbf {w}^{d} \right\Vert _{2}\括号${瓦12,...,瓦d2}来评估特征的重要性。在八个基准数据集上的实验结果表明所提出方法的优越性能。