  Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction
of nonnegative parts-based and physically meaningful latent components from
high-dimensional tensor data while preserving the natural multilinear structure
of data. However, as the data tensor often has multiple modes and is
large-scale, existing NTD algorithms suffer from a very high computational
complexity in terms of both storage and computation time, which has been one
major obstacle for practical applications of NTD. To overcome these
disadvantages, we show how low (multilinear) rank approximation (LRA) of
tensors is able to significantly simplify the computation of the gradients of
the cost function, upon which a family of efficient first-order NTD algorithms
are developed. Besides dramatically reducing the storage complexity and running
time, the new algorithms are quite flexible and robust to noise because any
well-established LRA approaches can be applied. We also show how nonnegativity
incorporating sparsity substantially improves the uniqueness property and
partially alleviates the curse of dimensionality of the Tucker decompositions.
Simulation results on synthetic and real-world data justify the validity and
high efficiency of the proposed NTD algorithms.
