# Tensor sparsification via a bound on the spectral norm of random tensors - Mathematics > Numerical Analysis

Tensor sparsification via a bound on the spectral norm of random tensors - Mathematics > Numerical Analysis - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

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.

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

Fuente: https://arxiv.org/