Several approximation algorithms for sparse best rank-1 approximation to higher-order tensors

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