Semi-supervised double sparse graphs based discriminant analysis for dimensionality reduction

Discriminant analysis (DA) is a well-known dimensionality reduction tool in pattern classification. With enough efficient labeled samples, the optimal projections could be found by maximizing the between-class scatter variance meanwhile minimizing the within-class scatter variance. However, the acquisition of label information is difficult in practice. So, semi-supervised discriminant analysis has attracted much attention in recent years, where both few labeled samples and many unlabeled samples are utilized during learning process. Sparse graph learned by sparse representation contains local structure information about data and is widely employed in dimensionality reduction. In this paper, semi-supervised double sparse graphs (sDSG) based dimensionality reduction is proposed, which considers both the positive and negative structure relationship of data points by using double sparse graphs. Aiming to explore the discriminant information among unlabeled samples, joint k nearest neighbor selection strategy is proposed to select pseudo-labeled samples which contain some precise discriminant information. In the following procedures, the data subset consisting of labeled samples and pseudo-labeled samples are used instead of the original data. Based on two different criterions, two sDSG based discriminant analysis methods are designed and denoted by sDSG-dDA (distance-based DA) and sDSG-rDA (reconstruction-based DA), which also use different strategies to reduce the effect of pseudo-labels' inaccuracy. Finally, the experimental results both on UCI datasets and hyperspectral images validate the effectiveness and advantage of the proposed methods compared with some classical dimensionality reduction methods.