  Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity
generalization of the dense tensor BR1Approx, and is a higher-order extension
of the sparse matrix BR1Approx, is one of the most important problems in sparse
tensor decomposition and related problems arising from statistics and machine
learning. By exploiting the multilinearity as well as the sparsity structure of
the problem, four approximation algorithms are proposed, which are easily
implemented, of low computational complexity, and can serve as initial
procedures for iterative algorithms. In addition, theoretically guaranteed
worst-case approximation lower bounds are proved for all the algorithms. We
provide numerical experiments on synthetic and real data to illustrate the
effectiveness of the proposed algorithms.
