High-Order Tensor Analysis Method for Information System Recommendations and Decisions

Tensor data (or multi-dimensional array data) are often generated in information systems of various industries, such as functional magnetic resonance imaging (fMRI) data in medicine systems and user-product data in product information systems. By using these data to predict the relationship between tensor features and univariate responses, data empowerment can be achieved, providing more accurate services or solutions, such as disease decision diagnosis or product recommendations. Currently available tensor regression methods, however, present two major shortcomings: the spatial information of tensors may be lost in these models, resulting in inaccurate prediction results; the calculation cost is too high, which results in untimely solutions or services. The two problems are more severe for large-scale data with high-order structures. Therefore, in order to achieve data empowerment, that is, to use tensor data to improve the quality and efficiency of information services or solutions, we propose sparse and low-rank tensor regression model (SLTR). This model enforces sparsity and low-rankness of the tensor coefficient by directly applying \mathscrl_1 norm and tensor nuclear norm on it respectively, such that not only the structural information of the tensor is preserved but also the data interpretation is convenient. To make the solving procedure scalable and efficient, SLTR makes use of the proximal gradient method to optimize the hybrid regularizer, which can be easily implemented parallelly. Additionally, a tight error bound of SLTR is theoretically proved. We evaluate SLTR on several simulated datasets and one video dataset. Experimental results show that, compared with previous models, SLTR is capable to obtain a better solution with much fewer time costs.