Nonlinear Locality-Preserving Projections With Dynamic Graph Learning

The affinity graph is regarded as a mathematical representation of the local manifold structure. The performance of locality-preserving projections (LPPs) and its variants is tied to the quality of the affinity graph. However, there are two drawbacks in current approaches. First, the pre-designed graph is inconsistent with the actual distribution of data. Second, the linear projection way would cause damage to the nonlinear manifold structure. In this article, we propose a nonlinear dimensionality reduction model, named deep locality-preserving projections (DLPPs), to solve these problems simultaneously. The model consists of two loss functions, each employing deep autoencoders (AEs) to extract discriminative features. In the first loss function, the affinity relationships among samples in the intermediate layer are determined adaptively according to the distances between samples. Since the features of samples are obtained by nonlinear mapping, the manifold structure can be kept in the low-dimensional space. Additionally, the learned affinity graph is able to avoid the influence of noisy and redundant features. In the second loss function, the affinity relationships among samples in the last layer (also called the reconstruction layer) are learned. This strategy enables denoised samples to have a good manifold structure. By integrating these two functions, our proposed model minimizes the mismatch of the manifold structure between samples in the denoising space and the low-dimensional space, while reducing sensitivity to the initial weights of the graph. Extensive experiments on toy and benchmark datasets have been conducted to verify the effectiveness of our proposed model.