Neighborhood discriminant tensor mapping

Linear dimensionality reduction (feature extraction) methods have been widely used in computer vision and pattern recognition. Two of the most representative methods are principal component analysis (PCA) and linear discriminant analysis (LDA  ). However, when dealing with a multidimensional dataset of dimension Rm1⊗Rm1⊗⋯⊗RmNRm1⊗Rm1⊗⋯⊗RmN (e.g. for images N=2N=2, videos N=3N=3), these methods usually first transform the original data to high dimensional vectors in Rm1×m2×⋯×mNRm1×m2×⋯×mN, and then analyze the data in such a high dimensional space. In this paper, we propose a supervised dimensionality reduction method called neighborhood discriminative tensor mapping (NDTM), which can directly process the multidimensional data as tensors. Moreover, NDTM can make use of the local information of the dataset to achieve a better classification result. Experimental results on face recognition show the superiority of our algorithm to traditional dimensionality reduction methods.