Low-rank nonnegative tensor approximation via alternating projections and sketching

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