Principal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms

1980/03/01 by Pieter M. Kroonenberg, Jan de Leeuw · 7 citations
Computer Science · Engineering · #Blind Source Separation Techniques #Advanced Adaptive Filtering Techniques #Control Systems and Identification

paper · doi:10.1007/bf02293599

openalex publication_date 1980/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

A new method to estimate the parameters of Tucker’s three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• A generalized inverse for matrices
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition

Cited by

• Tensor Completion Algorithms in Big Data Analytics
• A survey of multilinear subspace learning for tensor data
• Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation
• A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition
• MPCA: Multilinear Principal Component Analysis of Tensor Objects
• Tucker Tensor Decomposition on FPGA
• Multilinear subspace learning [wikipedia]