A novel estimation procedure for robust CANDECOMP/PARAFAC model fitting

The parameter estimation in CANDECOMP/PARAFAC (CP) is carried out by alternating least squares (ALS) that yields least-squares solutions and provides consistent outcomes. At the same time it has several drawbacks, like sensitivity to the presence of outliers in the data, issues with the computational efficiency in terms of processing time and memory requirements, as well as susceptibility to degeneracy conditions. These weaknesses have been addressed, but there is no outlier-robust procedure that at the same time is highly computationally efficient, especially for large data sets. A novel procedure based on an integrated estimation algorithm is proposed. This is an alternative to ALS, which guards against outliers and is computationally efficient at the same time. The performance of the new method is demonstrated on an extensive simulation study and an empirical example.