Data and Algebra Seminar

Tensors or multidimensional arrays, are higher-order generalizations of matrices that naturally represent data with inherent multi-way structure. Tensor rank decomposition is a key tool for uncovering hidden patterns in such data. In this talk, we introduce a novel algorithm based on generating polynomials to compute tensor decompositions. We prove that under certain rank conditions, our method recovers that exact decomposition. For higher ranks beyond this threshold, we provide an optimization-based variant that effectively detects the tensor decomposition. Numerical experiments illustrate the robustness and efficiency of our approach.