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Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsitygeneralization of the dense tensor BR1Approx, and is a higher-order extensionof the sparse matrix BR1Approx, is one of the most important problems in sparsetensor decomposition and related problems arising from statistics and machinelearning. By exploiting the multilinearity as well as the sparsity structure ofthe problem, four approximation algorithms are proposed, which are easilyimplemented, of low computational complexity, and can serve as initialprocedures for iterative algorithms. In addition, theoretically guaranteedworst-case approximation lower bounds are proved for all the algorithms. Weprovide numerical experiments on synthetic and real data to illustrate theeffectiveness of the proposed algorithms.

Several Approximation Algorithms for Sparse Best Rank-1 Approximation to Higher-Order Tensors