Canonical Rank Estimation Using Side Information, Application to Multidimensional Harmonic Retrieval

In this work, the canonical rank estimation for the rank- $R$ Canonical Polyadic (CP) model is investigated in the multiview context. In this scenario, we assume that we dispose of a set of noisy reshaping matrices of the tensor of interest enjoying the rank-keeping property. This means that the reshaping matrices are all rank- $R$. This is highly typical in tensor decomposition context. Our contribution is to reformulate the problem of interest into an alternative and intuitive formalism where the canonical rank is estimated thanks to a particular reshaping matrix and using the rest as side information in a binary classification procedure. Our approach allows to estimate the canonical rank in the noisy context and to “validate” this estimation without ground truth. Finally, we illustrate our methodology with the Minimum Description Length (MDL) criterion in the context of the Tensor Train-Hierarchical SVD (TT-HSVD) algorithm and apply it to the multidimensional harmonic retrieval problem.