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Analysis on Supervised Neighborhood Preserving Embedding

Neighborhood Preserving Embedding (NPE) is an unsupervised dimensionality reduction technique. Hence, it is lacking of discriminative capability. Zeng and Luo have proposed Supervised Neighborhood Preserving Embedding (SNPE), which uses class information of training samples to better describe data intrinsic structure. The robustness of SNPE has been demonstrated since it yields promising recognition results. However, there is no theoretical analysis to explain the good performance. Here, we show analytically that the neighborhood discriminant criterion, which manifested in the objective function of SNPE, is close resembled to Fisher discriminant criterion. SNPE is evaluated in ORL and PIE face databases. The inclusion of class information in data learning results superior performance of SNPE to NPE.