An efficient algorithm for Parafac with uncorrelated mode‐A components applied to large I × J × K data sets with I >> JK

Harshman and Lundy (Comput. Stat. Data Anal. 1994; 18: 39–72) described an option in the Parafac algorithm for constraining one or more component matrices to have uncorrelated columns. In cases where an algorithm using this constraint is to be applied to a three‐way array that has too many entries in one mode, the algorithm is computationally impractical. The present paper describes two modifications of their algorithm to handle the multiplications involving the large mode efficiently for cases where the product of the sizes of the other two modes is smaller than that of the larger mode. By means of a simulation study, it is demonstrated that these procedures (which are similarly efficient) are much more efficient than the original algorithm. Copyright © 2009 John Wiley & Sons, Ltd.