Neighborhood Preserving Non-negative Tensor Factorization for image representation

Non-negative Matrix Factorization (NMF) has become a powerful tool for image representation due to its enhanced semantic interpretability under non-negativity. Unfortunately, two types of neighborhood information essential to representation are lost in NMF. For individual image, the local structure information is missing in the vectorization, which can then be avoided by Non-negative Tensor Factorization (NTF). For image data points, they often reside on a low dimensional submanifold embedded in a high dimensional ambient space. NMF and NTF are incapable of encoding the local geometrical information, which can nevertheless be resuscitated by manifold learning. To simultaneously model both of the neighborhood relationship within and among image data, this paper proposes a novel algorithm called Neighborhood Preserving Non-negative Tensor Factorization (NPNTF) by incorporating locally linear embedding regularization into tensor factorization. Experimental results on image clustering show the superior performance of NPNTF with more natural and discriminating representation ability.