Fuzzy-rough Sets (FRS) provide an outstanding theoretical tool for Feature Selection (FS). Whilst promising, the FRS model is sensitive to noisy information and ineffectively applicable to the data with large class density difference, with existing FRS based FS methods only tackling one of these challenges. Therefore, to overcome both of these issues, this paper presents a robust FS algorithm using linear reconstruction measure for the first time. First, a pseudo FRS model is proposed, where the distribution aware linear reconstruction relation serving as the fuzzy similarity relation is constructed by considering the insight of meaningful information (i.e., distribution information of samples and density information of classes) to enhance the robustness and the pseudo fuzzy rough approximations are further redefined based on k Nearest Neighbor (kNN) granules determined by the linear reconstruction coefficients to empower the anti-noise ability. Then, the pseudo FRS model is employed to guide the robust FS algorithm from the perspective of redundant filter, strongly relevant priority and discriminative selection to determine the final feature subset. The experimental results on 31 datasets and practical applications (i.e., cancer diagnosis and face recognition) demonstrate that the reduct gained by the proposed approach generally outperforms those attained by alternative implementations of FRS-based FS and state-of-the-art FS techniques.

中文翻译：

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使用线性重构测量的鲁棒伪模糊粗糙特征选择


模糊粗糙集 (FRS) 为特征选择 (FS) 提供了出色的理论工具。虽然很有前景，但 FRS 模型对噪声信息敏感，并且不能有效地适用于类密度差异较大的数据，现有的基于 FRS 的 FS 方法只能解决这些挑战之一。因此，为了克服这两个问题，本文首次提出了一种使用线性重建测量的鲁棒FS算法。首先，提出了一种伪FRS模型，其中通过考虑有意义信息（即样本的分布信息和类的密度信息）的洞察来构建作为模糊相似关系的分布感知线性重建关系，以增强鲁棒性和基于线性重构系数确定的k个最近邻(kNN)颗粒进一步重新定义伪模糊粗略近似，以增强抗噪声能力。然后，利用伪FRS模型从冗余过滤、强相关优先级和判别性选择的角度指导鲁棒FS算法确定最终的特征子集。 31 个数据集和实际应用（即癌症诊断和人脸识别）的实验结果表明，所提出的方法所获得的减少量通常优于基于 FRS 的 FS 和最先进的 FS 技术的替代实现所获得的减少量。