Robust methods based on the hosvd for estimating the model order in PARAFAC models

Parallel factor (PARAFAC) analysis represents a decomposition of a tensor into a minimum sum of rank one tensors. For this task, one crucial problem is the estimation of the number of rank one components that are required to represent the tensor. This problem is also known as model order estimation. Recently we have developed new R-dimensional techniques based on the HOSVD to estimate the number of components in multi-dimensional harmonic retrieval problems (i.e., R-D EFT, R-D AIC, and R-D MDL). In this paper, we apply these R-D methods to the PARAFAC model, which is a more general multi-way data model, and show that they outperform T-CORCONDIA, a nonsubjective form of CORCONDIA, in terms of the probability of detection as well as the required computational complexity.