Low-Rank Tensor Recovery for Geo-Demand Estimation in Online Retailing

National retailers often rely on past sales data in their inventory allocation decisions where the understanding of the item-location-time specific demand (geo-demand) distributions is crucial. However, in many cases, errors and sparsity of the geo-demand data undermine the quality of data-driven decisions. It is thus important to recover the missing entries and identify errors. We organize the geo-demand data as a tensor in item, zone and time dimensions with a significant amount of missing entries. The problem is formulated as a robust low-rank tensor recovery problem in a convex optimization framework. We further propose a tailored optimization algo- rithm based on the alternating direction augmented Lagrangian method. By tests on synthetic data, the recovery performance and algorithm convergence are verified. Lastly, we demonstrate the framework with a real set of sales data from a major online retailer and investigate the effectiveness of the optimization framework both quantitatively and qualitatively.