Abstract
Least square regression (LSR) and principal component analysis (PCA) are two representative dimensionality reduction algorithms in the fields of machine learning. In this paper, we propose a novel method to jointly learn projections from the subspaces derived from the modified LSR and PCA. To implement simultaneous feature learning, we design a novel joint regression learning model by imposing two orthogonal constraints. Therefore, the learned projections can preserve the minimum reconstruction error and the discriminative information in the low-dimensional subspaces. Besides, since the traditional LSR and PCA are sensitive to the outliers, we utilize the robust L2,1-norm as the metric of loss function to improve the model’s robustness. A simple iterative algorithm is proposed to solve the proposed framework. Experiments on face databases show the promising performance of our method.
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