Generalized convex nonnegative tensor decomposition on statistical manifolds

Convex tensor decomposition methods based on information geometry typically restrict the selection of the e-flat submanifold to those parameterized in the natural parameter space. However, in theory, e-flat submanifolds that are not parameterized in the natural parameter space can also be employed for tensor decomposition, leading to projections of the empirical distribution onto alternative submanifolds, a possibility that has not been explored. Here we extend information geometric approaches for decomposing non-negative tensors by introducing an alternative parameterization for e-flat submanifolds. The resulting method, called General Nonnegative Convex Tensor Decomposition (GNCTD), enables us to perform an m-projection of the input tensor onto any e-flat submanifold within a log-linear model. We demonstrate the effectiveness of this approach in both tensor completion and approximation tasks.