In this paper, we propose a novel supervised manifold learning approach, supervised locality discriminant manifold learning (SLDML), for head pose estimation. Traditional manifold learning methods focus on preserving only the intra-class geometric properties of the manifold embedded in the high-dimensional ambient space, so they cannot fully utilize the underlying discriminative knowledge of the data. The proposed SLDML aims to explore both geometric structure and discriminant information of the data, and yields a smooth and discriminative low-dimensional embedding by adding the local discriminant terms in the optimization objectives of manifold learning. Moreover, for efficiently handling out-of-sample extension and learning with the local consistency, we decompose the manifold learning as a two-step approach. We incorporate the manifold learning and the regression with a learned discriminant manifold-based projection function obtained by discriminatively Laplacian regularized least squares. The SLDML provides both the low-dimensional embedding and projection function with better intra-class compactness and inter-class separability, therefore preserves the local geometric structures more effectively. Meanwhile, the SLDML is supervised by both biased distance and continuous head pose angle information when constructing the graph, embedding the graph and learning the projection function. Our experiments demonstrate the superiority of the proposed SLDML over several current state-of-art approaches for head pose estimation on the publicly available FacePix dataset. 
Supervised locality discriminant manifold learning for head pose estimation