Principal component analysis of three-mode data by means of alternating least squares algorithms

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.

On best rank-2 and rank-(2,2,2) approximations of order-3 tensors

“…Algorithms for solving problem (2.2) have been proposed in [35,36,37,38,31]. In the higher-order power method of [36] each iteration rotates mass to the target subtensor by using the singular value decomposition (SVD) of the columns of one of the three matrix unfoldings of the rotated tensor corresponding to the subtensor.…”

“…For (A) we use the ALS algorithm of [41] as is also done in [27]. For (C) we use the ALS algorithm of [35] as described in [36].…”

Visualization of competitive market structure by means of choice data

“…For the calculation of the Tucker3 model I applied the TuckALS3-algorithm proposed by Kroonenberg and de Leew (1980). For the initial solution of the algorithm, random matrices for A, B and C are used and the NIPALS-Algorithm applied for the SVD within each iteration,.…”

Multiway Filtering Based on Multilinear Algebra Tools

“…Indeed, the digital data obtained from these sensors are fundamentally higher order tensor objects, that is, multiway arrays whose elements are accessed via more than two indexes. Each index is associated with a dimension of the tensor generally called "n th -mode" [7,8,15,16]. For the last decades, the classical algebraic processing methods have been specifically developed for vector and matrix representations.…”