Tucker1 model algorithms for fast solutions to large PARAFAC problems

We describe a method of performing trilinear analysis on large data sets using a modification of the PARAFAC‐ALS algorithm. Our method iteratively decomposes the data matrix into a core matrix and three loading matrices based on the Tucker1 model. The algorithm is particularly useful for data sets that are too large to upload into a computer's main memory. While the performance advantage in utilizing our algorithm is dependent on the number of data elements and dimensions of the data array, we have seen a significant performance improvement over operating PARAFAC‐ALS on the full data set. In one case of data comprising hyperspectral images from a confocal microscope, our method of analysis was approximately 60 times faster than operating on the full data set, while obtaining essentially equivalent results. Copyright © 2008 by John Wiley & Sons, Ltd.