Wasserstein Nonnegative Tensor Factorization with Manifold Regularization
This work addresses feature extraction in nonnegative high-order data for applications like image or signal processing, but it is incremental as it builds on prior Wasserstein-based methods by extending them to tensors.
The paper tackled the problem of nonnegative tensor factorization (NTF) by proposing Wasserstein manifold nonnegative tensor factorization (WMNTF) to incorporate feature correlation and sample manifold information, resulting in improved performance over existing NMF and NTF methods as demonstrated experimentally.
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.