Correlation metric for generalized feature extraction

Beyond conventional linear and kernel-based feature extraction, we present a more generalized formulation for feature extraction in this paper. Two representative algorithms using the correlation metric are proposed based on this formulation. Correlation Embedding Analysis (CEA), which incorporates both correlational mapping and discriminant analysis, boosts the discriminating power by mapping the data from a high-dimensional hypersphere onto another low-dimensional hypersphere and preserving the neighboring relations with local-sensitive graph modeling. Correlational Principal Component Analysis (CPCA) generalizes the Principal Component Analysis (PCA) algorithm to the case with data distributed on a high-dimensional hypersphere. Their advantages stem from two facts: 1) directly working on normalized data, which are often the outputs from data preprocessing, and 2) directly designed with the correlation metric, which is shown to be generally better than euclidean distance for classification purpose in many real-world applications. Extensive visual recognition experiments compared with existing feature extraction algorithms demonstrate the effectiveness of the proposed algorithms. Index Terms--Feature extraction, graph embedding, correlation embedding analysis, correlational principal component analysis, face recognition.