Nonnegative Tucker decomposition with alpha-divergence

Nonnegative tucker decomposition (NTD) is a recent multiway extension of nonnegative matrix factorization (NMF), where nonnega- tivity constraints are incorporated into Tucker model. In this paper we consider alpha-divergence as a discrepancy measure and derive multiplicative updating algorithms for NTD. The proposed multiplicative algorithm includes some existing NMF and NTD algorithms as its special cases, since alpha-divergence is a one-parameter family of divergences which accommodates KL-divergence, Hellinger divergence, X² divergence, and so on. Numerical experiments on face images show how different values of alpha affect the factorization results under different types of noise.