Core consistency diagnostic aided by reconstruction error for accurate enumeration of the number of components in parafac models

Recently, the CORe CONsistency DIAgnostic (CORCONDIA) has attracted more and more attention as an effective tool for determining the number of components in parallel factor analysis (PARAFAC) or Tucker 3 models. In CORCONDIA, a proper user-defined threshold is required to ensure reliable performance. The optimal threshold increases with the signal-to-noise ratio (SNR), which results in significant probability of over-enumeration of the number of components for high SNRs under fixed threshold settings. We propose to first use a threshold interval to obtain lower and upper bounds of the estimates. The estimate takes the upper bound as its initial value and is then refined based on a sequence of hypothesis tests by exploiting the reconstruction error of the PARAFAC decomposition. The proposed scheme provides accurate detection for both low and high SNRs at almost no extra computational cost.