Normalized LDA for semi-supervised learning

Linear Discriminant Analysis (LDA) has been a popular method for feature extracting and face recognition. As a supervised method, it requires manually labeled samples for training, while making labeled samples is a time consuming and exhausting work. A semi-supervised LDA (SDA) has been proposed recently to enable training of LDA with partially labeled samples. In this paper, we first reformulate supervised LDA based on the normalized perspective of LDA. Then we show that such a reformulation is powerful for semi-supervised learning of LDA. We call this approach Normalized LDA, which uses total diversity to normalize intra-class diversity and aims to find projection directions that minimize normalized intra-class diversity. Although the Normalized LDA is identical to LDA in the supervised situation, a semi-supervised approach can be easily incorporated into its framework to make use of unlabeled samples to improve the performance in the learned subspace. Moreover, different with SDA which uses unlabeled samples to preserve neighboring relations, unlabeled samples in the Normalized LDA are used for a more accurate estimation of data space. Experiments of face recognition on the FRGC version 2 database and CMU PIE database demonstrate that the Normalized LDA outperforms SDA.