Multiple Dense Subtensor Estimation with High Density Guarantee

Dense subtensor detection is a well-studied area, with a wide range of applications, and numerous efficient approaches and algorithms have been proposed. Existing algorithms are generally efficient for dense subtensor detection and could perform well in many applications. However, the main drawback of most of these algorithms is that they can estimate only one subtensor at a time, with a low guarantee on the subtensor's density. While some methods can, on the other hand, estimate multiple subtensors, they can give a guarantee on the density with respect to the input tensor for the first estimated subsensor only. We address these drawbacks by providing both theoretical and practical solution for estimating multiple dense subtensors in tensor data. In particular, we guarantee and prove a higher bound of the lower-bound density of the estimated subtensors. We also propose a novel approach to show that there are multiple dense subtensors with a guarantee on its density that is greater than the lower bound used in the state-of-the-art algorithms. We evaluate our approach with extensive experiments on several real- world datasets, which demonstrates its efficiency and feasibility.