\(l_{2}\) -norm 2-directional 2-dimensional LDA ( \(\mathrm{(2D)}^2\) LDA) is an effective matrix-based supervised dimensionality reduction method by considering left-and-right side dimensionality reduction at the same time. However, \(\mathrm{(2D)}^2\) LDA maybe face the singularity issue when facing with the small sample size (SSS) problem. To cope with this issue, this paper proposes a novel bilateral two-dimensional linear discriminant analysis, called B2DLDA. The objective function of B2DLDA maximizes the matrix-based between-class distance and meanwhile minimizes the matrix-based within-class distance. Compared with \(\mathrm{(2D)}^2\) LDA, our B2DLDA is solved effectively through standard eigenvalue decomposition problems, which does not involve the inverse of a matrix and hence avoids the SSS problem. The experimental results on five image data sets demonstrate the effectiveness of B2DLDA.
