Conformal Embedding Analysis with Local Graph Modeling on the Unit Hypersphere

We present the Conformal Embedding Analysis (CEA) for feature extraction and dimensionality reduction. Incorporating both conformal mapping and discriminating analysis, CEA projects the high-dimensional data onto the unit hypersphere and preserves intrinsic neighbor relations with local graph modeling. Through the embedding, resulting data pairs from the same class keep the original angle and distance information on the hypersphere, whereas neighboring points of different class are kept apart to boost discriminating power. The subspace learned by CEA is gray-level variation tolerable since the cosine-angle metric and the normalization processing enhance the robustness of the conformal feature extraction. We demonstrate the effectiveness of the proposed method with comprehensive comparisons on visual classification experiments.