Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and

Abstract—This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local andnonlocal quantities.UDPcharacterizes the local scatter aswell as thenonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, Locality Preserving Projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposedmethod is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDAwhen the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications. Index Terms—Dimensionality reduction, feature extraction, subspace learning, Fisher linear discriminant analysis (LDA), manifold learning, biometrics, face recognition, palmprint recognition. Ç