Wasserstein Nonnegative Tensor Factorization with Manifold
  Regularization
Jianyu Wang Linruize Tang
Nonnegative tensor factorization (NTF) has become an important tool for
feature extraction and part-based representation with preserved intrinsic
structure information from nonnegative high-order data. However, the original
NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss
function which treats each feature equally leading to the neglect of the
side-information of features. To utilize correlation information of features
and manifold information of samples, we introduce Wasserstein manifold
nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein
distance between the distribution of input tensorial data and the distribution
of reconstruction. Although some researches about Wasserstein distance have
been proposed in nonnegative matrix factorization (NMF), they ignore the
spatial structure information of higher-order data. We use Wasserstein distance
(a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and
add a graph regularizer to a latent factor. Experimental results demonstrate
the effectiveness of the proposed method compared with other NMF and NTF
methods.