A soft label based linear discriminant analysis for semi-supervised dimensionality reduction

Dealing with high-dimensional data has always been a major problem with the research of pattern recognition and machine learning. And Linear Discriminant Analysis (LDA) is one of the most popular methods for dimensionality reduction. But it only uses labeled samples while neglect the unlabeled samples, which are abundant and can be easily obtained in the real world. In this paper, we propose a new dimensionality reduction method by using the unlabeled samples to enhance the performance of LDA. The new method first propagates the label information from labeled set to unlabeled set via a label propagation process, where the predicted labels of unlabeled samples, called soft labels, can be obtained. It then incorporates the soft labels into the construction of scatter matrixes to find a transformed matrix for dimensionality reduction. In this way, the proposed method can preserve more discriminative information, which is good when solving the classification problem. Extensive simulations are carried based several datasets and the results show the effectiveness of the proposed method.