Fast and Efficient Algorithms for Nonnegative Tucker Decomposition

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In this paper, we propose new and efficient algorithms for nonnegative Tucker decomposition (NTD): Fast α-NTD algorithm which is much precise and faster than α-NTD [1]; and β-NTD algorithm based on the β divergence. These new algorithms include efficient normalization and initialization steps which help to reduce considerably the running time and increase dramatically the performance. Moreover, the multilevel NTD scheme is also presented, allowing further improvements (almost perfect reconstruction). The performance was also compared to other well-known algorithms (HONMF, HOOI, ALS algorithms) for synthetic and real-world data as well.