Faster Robust Tensor Power Method for Arbitrary Order

With the development of large-scale-data-driven applications, such as neural networks, social network analysis, and multi-media processing, tensors have become a powerful paradigm to handle the data. According to [SWZ16], in recommendation systems, it's often beneficial to utilize more than two attributes to generate more accurate recommendations. For instance, in the case of Groupon, one could examine three attributes such as time, users, and activities, which may include but are not limited to the factors like time of day, season, weekday, weekend, etc., as a basis for making predictions. More information on this can be found in [KB09]. Tensor decomposition is a mathematical tool that can break down the higher order tensor into a combination of lower order tensors. To deal with the high-dimensional data, decomposition becomes a natural method to handle the tensors, where the operation reads the original tensor as inputs and outputs the decomposition of it in some succinct form.