Locality preserving projections (LPP) is a recently developed linear-feature extraction algorithm that has been frequently used in the task of face recognition and other applications. However, LPP does not satisfy the shift-invariance property, which should be satisfied by a linear-feature extraction algorithm. In this paper, we analyze the reason and derive the shift-invariant LPP algorithm. Based on the analysis of the geometrical meaning of the shift-invariant LPP algorithm, we propose two algorithms to minimize the locality and maximize the globality under an orthogonal projection matrix. Experimental results on face recognition are presented to demonstrate the effectiveness of the proposed algorithms.
This paper proposes a novel semi-supervised dimensionality reduction learning algorithm for the ranking problem.
Generally, we do not make the assumption of existence of classes and do not want to find the classification
boundaries. Instead, we only assume that the data point cloud can construct a graph which describes the
manifold structure, and there are multiple concepts on different parts of the manifold. By maximizing the distance
between different concepts and simultaneously preserving the local structure on the manifold, the learned metric
can indeed give good ranking results. Moreover, based on the theoretical analysis of the relationship between
graph Laplacian and manifold Laplace-Beltrami operator, we develop an online learning algorithm that can
incrementally learn the unlabeled data.