Learning from local and global discriminative information for semi-supervised dimensionality reduction

Semi-supervised dimensionality reduction is an important research topic in many pattern recognition and machine learning applications. Among all the methods for semi-supervised dimensionality reduction, SDA and LapRLS are two popular ones. Though the two methods are actually the extensions of different supervised methods, we show in this paper that they can be unified into a regularized least square framework. However, the regularization term added to the framework focuses on smoothing only, it cannot fully utilize the underlying discriminative information which is vital for classification. In this paper, we propose a new effective semi-supervised dimensionality reduction method, called LLGDI, to solve the above problem. The proposed LLGDI method introduces a discriminative manifold regularization term by using the local discriminative information instead of only relying on neighborhood information. In this way, both the local geometrical and discriminative information of dataset can be preserved by the proposed LLGDI method. Theoretical analysis and extensive simulations show the effectiveness of our algorithm. The results in simulations demonstrate that our proposed algorithm can achieve great superiority compared with other existing methods.