An Efficient Algorithm for PARAFAC of Three-Way Data with Large Numbers of Observation Units | Psychometrika | Cambridge Core (original) (raw)

Abstract

The CANDECOMP algorithm for the PARAFAC analysis of n × m × p three-way arrays is adapted to handle arrays in which n > mp more efficiently. For such arrays, the adapted algorithm needs less memory space to store the data during the iterations, and uses less computation time than the original CANDECOMP algorithm. The size of the arrays that can be handled by the new algorithm is in no way limited by the number of observation units (n) in the data.

References

Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition. Psychometrika, 35, 283–319.CrossRefGoogle Scholar

Harshman, R. A. (1970). Foundations of the PARAFAC procedure: Models and conditions for an “explanatory” multi-mode factor analysis. UCLA Working Papers in Phonetics, 16, 1–84.Google Scholar

Harshman, R. A. (1972). PARAFAC2: Mathematical and technical notes. UCLA Working Papers in Phonetics, 22, 31–44.Google Scholar

Harshman, R. A., & Lundy, M. E. (1984). Data preprocessing and the extended PARAFAC model. In Law, H. G., Snyder, C. W., Hattie, J. A., & McDonald, R. P. (Eds.), Research methods for multimode data analysis (pp. 216–284). New York: Praeger.Google Scholar

Harshman, R. A., & Lundy, M. E. (1984). The PARAFAC model for three-way factor analysis and multidimensional scaling. In Law, H. G., Snyder, C. W., Hattie, J. A., & McDonald, R. P. (Eds.), Research methods for multimode data analysis (pp. 122–215). New York: Praeger.Google Scholar

Kroonenberg, P. M. (1983). Three-mode principal component analysis, Leiden: DSWO Press.Google Scholar