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Beyond linear and kernel-based feature extraction, we propose in this paper the generalized feature extraction formulation based on the so-called graph embedding framework. Two novel correlation metric based algorithms are presented based on this formulation. correlation embedding analysis (CEA), which incorporates both correlational mapping and discriminating analysis, boosts the discriminating power by mapping data from a high-dimensional hypersphere onto another low-dimensional hypersphere and preserving the intrinsic neighbor relations with local graph modeling. correlational principal component analysis (CPCA) generalizes the conventional Principal Component Analysis (PCA) algorithm to the case with data distributed on a high-dimensional hypersphere. Their advantages stem from two facts: 1) tailored to normalized data, which are often the outputs from the data preprocessing step, and 2) directly designed with correlation metric, which shows to be generally better than Euclidean distance for classification purpose. Extensive comparisons with existing algorithms on visual classification experiments demonstrate the effectiveness of the proposed algorithms.