Locality adaptive discriminant analysis

Linear Discriminant Analysis (LDA) is a popular technique for supervised dimensionality reduction, and its performance is satisfying when dealing with Gaussian distributed data. However, the neglect of local data structure makes LDA inapplicable to many real-world situations. So some works focus on the discriminant analysis between neighbor points, which can be easily affected by the noise in the original data space. In this paper, we propose a new supervised dimensionality reduction method, Locality Adaptive Discriminant Analysis (LADA), to learn a representative subspace of the data. Compared to LDA and its variants, the proposed method has three salient advantages: (1) it finds the principle projection directions without imposing any assumption on the data distribution; (2) it's able to exploit the local manifold structure of data in the desired subspace; (3) it exploits the points' neighbor relationship automatically without introducing any additional parameter to be tuned. Performance on synthetic datasets and real-world benchmark datasets demonstrate the superiority of the proposed method.