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We present an efficient low-rank approximation algorithm for non-negativetensors. The algorithm is derived from our two findings: First, we show thatrank-1 approximation for tensors can be viewed as a mean-field approximation bytreating each tensor as a probability distribution. Second, we theoreticallyprovide a sufficient condition for distribution parameters to reduce Tuckerranks of tensors; interestingly, this sufficient condition can be achieved byiterative application of the mean-field approximation. Since the mean-fieldapproximation is always given as a closed formula, our findings lead to a fastlow-rank approximation algorithm without using a gradient method. Weempirically demonstrate that our algorithm is faster than the existingnon-negative Tucker rank reduction methods and achieves competitive or betterapproximation of given tensors.

Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation