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Nonnegative tensor factorization (NTF) has become an important tool forfeature extraction and part-based representation with preserved intrinsicstructure information from nonnegative high-order data. However, the originalNTF methods utilize Euclidean or Kullback-Leibler divergence as the lossfunction which treats each feature equally leading to the neglect of theside-information of features. To utilize correlation information of featuresand manifold information of samples, we introduce Wasserstein manifoldnonnegative tensor factorization (WMNTF), which minimizes the Wassersteindistance between the distribution of input tensorial data and the distributionof reconstruction. Although some researches about Wasserstein distance havebeen proposed in nonnegative matrix factorization (NMF), they ignore thespatial structure information of higher-order data. We use Wasserstein distance(a.k.a Earth Mover's distance or Optimal Transport distance) as a metric andadd a graph regularizer to a latent factor. Experimental results demonstratethe effectiveness of the proposed method compared with other NMF and NTFmethods.

Wasserstein Nonnegative Tensor Factorization with Manifold Regularization