Shifted factor analysis—Part II: Algorithms
Sungjin Hong, Richard A. Harshman · Journal of Chemometrics · 2003
Abstract We previously proposed a family of models that deal with the problem of factor position shift in sequential data. We conjectured that the added information provided by fitting the shifts would make the model parameters identifiable, even for two‐way data. We now derive methods of parameter estimation and give the results of experiments with synthetic data. The alternating least squares (ALS) approach is not fully suitable for estimation, because factor position shifts destroy the multilinearity of the latent structure. Therefore an alternative ‘quasi‐ALS’ approach is developed, some of its practical and theoretical properties are dealt with and several versions of the quasi‐ALS algorithm are described in detail. These procedures are quite computation‐intensive, but analysis of synthetic data demonstrates that the algorithms can recover shifting latent factor structure and, in the situations tested, are robust against high error levels. The results of these experiments also provide strong empirical support for our conjecture that the two‐way shifted factor model has unique solutions in at least some circumstances. Copyright © 2003 John Wiley & Sons, Ltd.