  Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or
Kullback-Leibler divergence between the original data and its low-rank
approximation which often suffers from grossly corruptions or outliers and the
neglect of manifold structures of data. In particular, NTF suffers from
rotational ambiguity, whose solutions with and without rotation transformations
are equally in the sense of yielding the maximum likelihood. In this paper, we
propose three Robust Manifold NTF algorithms to handle outliers by
incorporating structural knowledge about the outliers. They first applies a
half-quadratic optimization algorithm to transform the problem into a general
weighted NTF where the weights are influenced by the outliers. Then, we
introduce the correntropy induced metric, Huber function and Cauchy function
for weights respectively, to handle the outliers. Finally, we introduce a
manifold regularization to overcome the rotational ambiguity of NTF. We have
compared the proposed method with a number of representative references
covering major branches of NTF on a variety of real-world image databases.
Experimental results illustrate the effectiveness of the proposed method under
two evaluation metrics (accuracy and nmi).
