  Currently, the size of scientific data is growing at an unprecedented rate.
Data in the form of tensors exhibit high-order, high-dimensional, and highly
sparse features. Although tensor-based analysis methods are very effective, the
large increase in data size makes the original tensor impossible to process.
Tensor decomposition decomposes a tensor into multiple low-rank matrices or
tensors that can be exploited by tensor-based analysis methods. Tucker
decomposition is such an algorithm, which decomposes a $n$-order tensor into
$n$ low-rank factor matrices and a low-rank core tensor. However, most Tucker
decomposition methods are accompanied by huge intermediate variables and huge
computational load, making them unable to process high-order and
high-dimensional tensors.
  In this paper, we propose FasterTucker decomposition based on FastTucker
decomposition, which is a variant of Tucker decomposition. And an efficient
parallel FasterTucker decomposition algorithm cuFasterTucker on GPU platform is
proposed. It has very low storage and computational requirements, and
effectively solves the problem of high-order and high-dimensional sparse tensor
decomposition. Compared with the state-of-the-art algorithm, it achieves a
speedup of around $15X$ and $7X$ in updating the factor matrices and updating
the core matrices, respectively.
