Low-rank constraint based dual projections learning for dimensionality reduction

Subspace learning is a widely-used fundamental method for feature extraction in several fields. Existing subspace-based methods only concentrate on projecting all data into a single subspace to achieve feature extraction. However, there are not only one task of the projection matrix to handle in majority existing methods. And it always need to deal multiple tasks (e.g., dimensional reduction, data similarity preservation, etc.), leading to the over-pressure for the single subspace and degrade the accuracy of the model. In order to deal with this issue, a dual representation locality preserving projection (DRLPP for short) is presented in this paper, in which dual different projection matrices are introduced to better accomplish multiple tasks. Specially, these two projection matrices are relaxed into a flexible form to select appropriate features for preserving the important properties of data. Meanwhile, as the two matrices share the same tasks, the structure of matrices and the corresponding projected data contain intrinsic geometric structure. Then, a structural similarity term and a linear subspace reconstruction term are proposed to deeply capture the potential relationship and maintain a suitable similarity of projected data. Moreover, a low-rank constraint is imposed to preserve the similarity between the two matrices and reduce the noise disturbance. Finally, an iterative algorithm with fast convergence is proposed to solve the corresponding optimization problem. Experimental results on five datasets demonstrate the effectiveness of the proposed method.