Tensor sparsification as a way to do dimensionality reduction:

Tensor sparsification via a bound on the spectral norm of random tensors by Nam H. Nguyen, Petros Drineas, Trac D. Tran

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 all sufficiently small elements of $\tensor A$, keeps all sufficiently large elements of $\tensor A$, and retains some of the remaining elements with probabilities proportional to the square of their magnitudes. We analyze the approximation accuracy of the proposed algorithm using a powerful inequality that we derive. This inequality bounds the spectral norm of a random tensor and is of independent interest. As a result, we obtain novel bounds for the tensor sparsification problem.

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