Dealing with high-dimensional data has always been a major problem in the research of pattern recognition and machine learning. Among all the dimensionality reduction techniques, Linear Discriminant Analysis (LDA) is one of the most popular methods that have been widely used in many classification applications. But LDA can only utilize 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 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 preferable when solving the classification problem. Extensive simulations are conducted on several datasets and the results show the effectiveness of the proposed method. 
Soft label based Linear Discriminant Analysis for image recognition and retrieval