A novel trilinear decomposition algorithm for second-order linear calibration

A novel trilinear decomposition algorithm for second-order linear calibration called self-weighted alternating trilinear decomposition (SWATLD) has been designed in this paper. Experiments show SWATLD has the features of fast convergence and being insensitive to the excess factors used in calculation. Due to the unique optimizing scheme employed, SWATLD is much more efficient than the ordinary PARAFAC algorithm. In terms of the variance, the performance of SWATLD is very stable when the number of factors used in calculation varies (as long as it is no less than the actual number of factors). Such a feature will facilitate the analysis of three-way data arrays, since it is now unnecessary to spend a lot of time and effort to accurately determine the number of underlying factors in the system studied as does in PARAFAC. Furthermore, as far as the deviations of the results are concerned, experiments show SWATLD can supply acceptable results in most cases.