Semi-supervised Discriminant Analyze with Instance-Level Constraints

Traditional linear discriminant analysis (LDA) is a popular dimensionality reduction method which preserve class separability. The method needs the labeled data to train. However in real worlds, the labeled training examples are very few but there are sufficient unlabeled data examples, so some former work (SDA) has made use the unlabeled training examples to do dimensionality reduction. But sometimes, there exits another kind of domain knowledge: the instances level constraints. In this paper, we consider the case when there are some useful instance level constraints. We propose a novel algorithm semi-supervised discriminant analyze with constraints (SDAC) which use three kinds of data: very few labeled data examples, sufficient unlabeled data examples and the instance level constraints. Our algorithm can be viewed as a constraint extension of traditional SDA algorithm. Experiments have been presented for semi-supervised classification tasks and have shown the effectiveness of our algorithm.