鲁棒联合稀疏不相关回归

Robust Joint Sparse Uncorrelated Regression

常见的无监督特征选择方法考虑的只是选择具有判别性的特征,而忽略了特征的冗余性,并且没有考虑到小类问题,故而影响到分类性能。基于此背景,提出鲁棒不相关回归算法。首先,对不相关回归进行研究,使用不相关正交约束,以便找出不相关但具有判别性的特征,不相关约束使得数据结构保持在Stiefel流形中,使模型具有封闭解,避免了传统的岭回归模型引发的可能的平凡解。其次,损失函数与正则化项使用L_(2,1)范数,保证模型的鲁棒性,得到具有稀疏性的投影矩阵;同时将小类问题考虑进去,使投影矩阵数量不受类别数的限制,得到足够多的投影矩阵,从而提升模型的分类性能。理论分析和多个数据集上的实验结果表明,所提出的方法比其他特征选择方法具有更好的性能。

Common unsupervised feature selection methods only consider the selection of discriminative features,while ignoring the redundancy of features and failing to consider the problem of small classes,which affect the classification performance.Based on this background,a robust uncorrelated regression algorithm is proposed.First,research on uncorrelated regression,use uncorrelated orthogonal constraints to find irrelevant but discriminative features.Uncorrelated constraints keep the data structure in the Stiefel manifold,making the model have a closed solution,avoiding the possible trivial solutions caused by the traditional ridge regression model.Secondly,the loss function and the regularization term use the L_(2,1)norm to ensure the robustness of the model and obtain a sparse projection matrix.At the same time,the small class problem is taken into account,so that the number of projection matrices is not limited by the number of classes,and the result is enough projection matrices to improve the classification performance of the model.Theoretical analysis and experimental results on multiple data sets show that the proposed method has better performance than other feature selection methods.