Effective Tensor Sketching via Sparsification

In this article, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, propose a novel tensor algorithm that retains subset of the entries in judicious way, and prove it can attain given level approximation accuracy terms spectral norm with much smaller sample complexity when compared existing approaches. particular, show k th order $ {d}\times \cdots \times {d}$ cubic xmlns:xlink="http://www.w3.org/1999/xlink">stable rank {r}_{ {s}}$ , size requirement achieving relative error notation="LaTeX">$\varepsilon $ is, up to logarithmic factor, {s}}^{1/2} {d}^{ {k}/2} /\varepsilon is relatively large, {s}} {d} ^{2}$ essentially optimal sufficiently small. It especially noteworthy an independent . To further demonstrate utility our techniques, also study how higher singular value decomposition (HOSVD) large tensors be efficiently approximated sparsification.