Nuclear-Norm-Based Jointly Sparse Regression for Two-Dimensional Image Regression

Haosheng Su, Zhihui Lai, Ning Liu, Jun Wan

Abstract: As a typical manifold learning method, two-dimensional Locality Preserving Projections (2DLPP) can perverse the intrinsic manifold structure of the data, and it has been widely used in dimensionality reduction. However, 2DLPP is sensitive to noise and outliers since 2DLPP uses the Frobenius norm to measure the reconstruction error. In order to address the robustness problem in 2DLPP, this paper proposes a novel framework, called nuclear-norm-based jointly sparse regression (NJSR). NJSR characterizes the reconstruction error by using the nuclear norm as the measurement and the \( L_{2,1} \)-norm as the regularized term to derive jointly sparse solutions for feature extraction and selection. Moreover, we propose a bilateral extension over NJSR called Bilateral NJSR (BNJSR). BNJSR learns the projection matrices in both the row and the column directions simultaneously. Both the NJSR and BNJSR can be solved through an iterative algorithm by computing a set of eigenfunctions. Two face databases are used to verify the effectiveness of the proposed methods, and the experimental results show BNJSR outperformed the compared methods.