Sparse robust adaptive unsupervised subspace learning for dimensionality reduction

This work is devoted to the investigation of dimension reduction problem. As an efficient dimension reduction method, much attention has been paid on unsupervised subspace learning since it does not rely on expensive labels. Firstly, we implant a robust estimator in the error term of objective function, this leads to that small coefficients can be automatically allocated to the abnormal points. Thus, our model is robust to noise and outliers. Posteriorly, the L 2, r -norm ( 1 ≤ r ≤ 2 ) is used as a measure of error, then, the performance of the model can be improved by selecting the appropriate adaptive parameter r. Further, a L 2, p -norm ( 0 < p ≤ 1 ) regularization term is added to the objective function, therefore the gained sparse subspace can further improve the efficiency and accuracy of the expression, as well as enhance the generalization ability of the model and reduce over-fitting. Moreover, an efficient algorithm with fast convergence speed is designed to solve the model. Finally, the experimental results on 14 datasets show that the subspace dimension obtained by our method is no more than 6. From the results of classification test, our algorithm has obvious advantages over the other similar six algorithms.

Authors

• Weizhi Xiong
• Guolin Yu
• Jun Ma University of Electronic Science and Technology of China
• Sheng Liu Zhejiang University of Technology

Keywords

• Unsupervised subspace learning
• Robust estimator
• L 2, p-norm regularization
• Sparse
• Dimensionality reduction