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Locality Preserving Projection (LPP) aims to preserve the local structure of the image space, while Principal Component Analysis (PCA) aims to preserve the global structure of the image space; LPP is linear, while Isomap, LLE, and Laplacian Eigenmap are nonlinear methods, so they yield maps that are defined only on the training data point and how to evaluate the maps on novel test data point remains unclear. Locally Discriminating Projection (LDP) is the extension of LPP, which seeks to preserve the intrinsic geometry structure by learning a locality preserving submanifold. LDP is a new subspace feature extraction method and supervised because it considers both class and label information. LDP performs much better than the other feature extraction methods such as PCA and Laplacian faces.
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