基于超图的稀疏属性选择算法*

针对噪声或者离群点通常会增加矩阵的秩的问题，提出一个在低秩限制下的基于超图的稀疏属性选择算法。具体地，该算法首先利用其他属性稀疏地表达每一个属性来获得属性自表达系数矩阵。然后，利用超图正则化因子获取数据的局部结构将子空间学习嵌入到属性选择的框架中。同时，利用范数惩罚自表达系数矩阵和损失函数，挖掘出属性之间的关系和样本间的关系来帮助算法有效地进行属性选择，最终提高模型的预测能力。在UCI数据集上的实验结果表明，该算法相比其它对比算法，能更有效地选取重要属性，并取得很好的分类效果。

Hypergraph-based Sparse Feature Selection

It is a fact that, during real data mining applications, noises or outliers can increase the rank of a matrix. This paper proposed a novel feature selection via hypergraph-based sparse structure combined with a low-rank constraint. Specially, the self-representation coefficient matrix was obtained through sparsely represent each feature by other features. Then, the local structure of the data was obtained via a hypergraph-based regularizer, so as to integrate the subspace learning into the framework of feature selection. Meanwhile, the correlation between features was obtained via using an norm regularization to penalize the self-representation matrix. And the norm on the loss function was designed for building the relation among samples. The correlation and relation were used for selecting those features that assisted in improving the performance. Experimental results demonstrate that the proposed method is much better than extant methods at classification performance and stability.