C2DNDA: A Deep Framework for Nonlinear Dimensionality Reduction

Dimensionality reduction has attracted much research interest in the past few decades. Existing dimensionality reduction methods like linear discriminant analysis and principal component analysis have achieved promising performance, but the single and linear projection properties limit further improvements of performance. A novel convolutional two-dimensional nonlinear discriminant analysis method is proposed for dimensionality reduction in this article. In order to handle nonlinear data properly, we present a newly designed structure with convolutional neural networks (CNNs) to realize an equivalent objective function with classical two-dimensional linear discriminant analysis (2DLDA) and thus embed the original 2DLDA into an end-to-end network. In this way, the proposed dimensionality reduction network can utilize the nonlinearity of the CNN and benefit from the learning ability. The results of experiment on different image-related applications demonstrate that our method outperforms other comparable approaches, and its effectiveness is proved.