Dimension reduction of multimodal data by auto-weighted local discriminant analysis

Dimension reduction technology is playing an increasingly important role in machine learning. One of the most important reduction technologies is linear discriminant analysis (LDA), but the main disadvantage of LDA is that it is unable to find the local manifold structure, which means that it may fail to dispose of multimodal data. However, high-dimensional multimodal data are ubiquitous in many rations. In this paper, we propose a new dimensionality reduction method called auto-weighted local discriminant analysis (ALDA). Our method learns the similarity matrix and updates in the subspace simultaneously so that the neighborships can be evaluated in the optimal subspaces instead of in the original space. Furthermore, the new model is built based on the ℓ_2,1-norm and automatically assigns a small weight to the pairwise points with large distance, and vice versa; thus, the local structure information can be captured by the ALDA. Additionally, an iterative re-weighted optimization algorithm is provided to efficiently solve the proposed model. Finally, extensive experiments conducted on several benchmark datasets and some synthetic datasets demonstrate the effectiveness of ALDA when comparing with some state-of-the-art dimensionality reduction methods.