  We show how to construct nonnegative low-rank approximations of nonnegative
tensors in Tucker and tensor train formats. We use alternating projections
between the nonnegative orthant and the set of low-rank tensors, using STHOSVD
and TTSVD algorithms, respectively, and further accelerate the alternating
projections using randomized sketching. The numerical experiments on both
synthetic data and hyperspectral images show the decay of the negative elements
and that the error of the resulting approximation is close to the initial error
obtained with STHOSVD and TTSVD. The proposed method for the Tucker case is
superior to the previous ones in terms of computational complexity and decay of
negative elements. The tensor train case, to the best of our knowledge, has not
been studied before.
