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Abstract: Given an order-$d$ tensor $\tensor A \in \R^{n \times n \times

.\times n}$,we present a simple, element-wise sparsification algorithm that zeroes out allsufficiently small elements of $\tensor A$, keeps all sufficiently largeelements of $\tensor A$, and retains some of the remaining elements withprobabilities proportional to the square of their magnitudes. We analyze theapproximation accuracy of the proposed algorithm using a powerful inequalitythat we derive. This inequality bounds the spectral norm of a random tensor andis of independent interest. As a result, we obtain novel bounds for the tensorsparsification problem.



Author: Nam H. Nguyen, Petros Drineas, Trac D. Tran

Source: https://arxiv.org/







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