Graph-optimized locality preserving projections

Locality preserving projections (LPP) is a typical graph-based dimensionality reduction (DR) method, and has been successfully applied in many practical problems such as face recognition. However, LPP depends mainly on its underlying neighborhood graph whose construction suffers from the following issues: (1) such neighborhood graph is artificially defined in advance, and thus does not necessary benefit subsequent DR task; (2) such graph is constructed using the nearest neighbor criterion which tends to work poorly due to the high-dimensionality of original space; (3) it is generally uneasy to assign appropriate values for the neighborhood size and heat kernel parameter involved in graph construction. To address these problems, we develop a novel DR algorithm called Graph-optimized Locality Preserving Projections (GoLPP). The idea is to integrate graph construction with specific DR process into a unified framework, which results in an optimized graph rather than predefined one. Moreover, an entropy regularization term is incorporated into the objective function for controlling the uniformity level of the edge weights in graph, so that a principled graph updating formula naturally corresponding to conventional heat kernel weights can be obtained. Finally, the experiments on several publicly available UCI and face data sets show the feasibility and effectiveness of the proposed method with encouraging results.