Self-Weighted Adaptive Locality Discriminant Analysis

The linear discriminant analysis (LDA) is a popular technique for dimensionality reduction, nevertheless, when the input data lie in a complicated geometry distribution, LDA tends to obtain undesired results since it neglects the local structure of data. Though plenty of previous works devote to capturing the local structure, they have the same weakness that the neighbors found in the original data space may be not reliable, especially when noise is large. In this paper, we propose a novel supervised dimensionality reduction approach, Self-weighted Adaptive Locality Discriminant Analysis (SALDA), which aims to find a representative low-dimensional subspace of data. Compared with LDA and its variants, SALDA explores the neighborhood relationship of data points in the desired subspace effectively. Besides, the weights between within-class data points are learned automatically without setting any additional parameter. Extensive experiments on synthetic and real-world datasets show the effectiveness of the proposed method.