  Various tensor decomposition methods have been proposed for data compression.
In real world applications of the tensor decomposition, selecting the tensor
shape for the given data poses a challenge and the shape of the tensor may
affect the error and the compression ratio. In this work, we study the effect
of the tensor shape on the tensor decomposition and propose an optimization
model to find an optimum shape for the tensor train (TT) decomposition. The
proposed optimization model maximizes the compression ratio of the TT
decomposition given an error bound. We implement a genetic algorithm (GA)
linked with the TT-SVD algorithm to solve the optimization model. We apply the
proposed method for the compression of RGB images. The results demonstrate the
effectiveness of the proposed evolutionary tensor shape search for the TT
decomposition.
