Tensor Decomposition via Simultaneous Power Iteration

Tensor decomposition is an important problem with many applications across several disciplines, and a popular approach for this problem is the tensor power method. However, previous works with theoretical guarantee based on this approach can only find the top eigenvectors one after one, unlike the case for matrices. In this paper, we show how to find the eigenvectors simultaneously with the help of a new initialization procedure. This allows us to achieve a better running time in the batch setting, as well as a lower sample complexity in the streaming setting.