Fast Tucker Factorization for Large-Scale Tensor Completion

Tensor completion is the task of completing multi-aspect data represented as a tensor by accurately predicting missing entries in the tensor. It is mainly solved by tensor factorization methods, and among them, Tucker factorization has attracted considerable interests due to its powerful ability to learn latent factors and even their interactions. Although several Tucker methods have been developed to reduce the memory and computational complexity, the state-of-the-art method still 1) generates redundant computations and 2) cannot factorize a large tensor that exceeds the size of memory. This paper proposes FTcom, a fast and scalable Tucker factorization method for tensor completion. FTcom performs element-wise updates for factor matrices based on coordinate descent, and adopts a novel caching algorithm which stores frequently-required intermediate data. It also uses a tensor file for disk-based data processing and loads only a small part of the tensor at a time into the memory. Experimental results show that FTcom is much faster and more scalable compared to all other competitors. It significantly shortens the training time of Tucker factorization, especially on real-world tensors, and it can be executed on a billion-scale tensor which is bigger than the memory capacity within a single machine.