Graph regularized discriminative nonnegative tucker decomposition for tensor data representation

Tensor factorization has been widely applied in computer vision and machine learning area. Nonnegative Tucker decomposition (NTD) is a popular tensor factorization technique. However, it neglects the geometrical structure of the data space and the available label information of sample data, lowering the data representation performance. To overcome this defect, in this paper, we propose a novel semi-supervised NTD method, named graph regularized discriminative nonnegative Tucker decomposition (GDNTD), which incorporates the graph construction of the data space and the available label information of the sample data into NTD. Specifically, a graph construction is utilized to preserve the geometric structure between data by a graph regularization term. Then, a label matrix is presented for guiding the data representation by a label constraint regularization term. Finally, based on the NTD property of maintaining the internal structure of data, the graph regularizer and the label regularizer are integrated into NTD to generate the proposed method. Thus, GDNTD can extract the part-based representation, preserve the local geometrical structure of the data space, and improve the discriminative ability of the learned model simultaneously, greatly boosting the model's data representation performance. We test the proposed method through a set of evaluations on four image datasets. Experimental results show that the GDNTD method outperforms state-of-the-art approaches, demonstrating its strong potential for data representation.