Research Seminar

Shifted and Warped Factor Analysis


Sungjin Hong


University of Illinois, Urbana-Champaign

Abstract: Misalignment of 1D sequential data has long been a stimulating problem since Cattell proposed a time-corrected P-technique in 1963. Sequential data are defined here as quantitative data that are collected along a meaningful sequence (e.g., J variables measured at I time points or multi-way data with one sequential mode), and misalignment means that the sequence is not comparable across the J variables.

From a component analysis point of view, most techniques proposed for the misalignment problem can be considered as a data preprocessing tool prior to the usual component/factor analysis, including the time-corrected P-technique itself. In contrast, Shifted Factor Analysis (SFA) defines data misalignment as a consequence of the position shifts of sequential components, allowing for a latent-level adjustment for the misalignment.

Sometimes, misalignment takes a more complex form, in that localized regions of data profiles are stretched or compressed distinctively from one profile to another. Warped Factor Analysis (WFA) quantifies this type of flexible shape changes by a linear warping of segmented components.

One may consider two- and three-way SFA/WFA models as adapted forms of, respectively, the principal component and the PARAFAC model so as to deal properly with position/shape misalignment at the latent level. Thanks to the added model structure for the alignment of sequential components, the two-way SFA and WFA models are unique (i.e., free of rotational ambiguity), unlike two-way component/factor models.

Algorithms developed for SFA and WFA are based on an alternating least squares (ALS) procedure. However, due to the provision for the latent-level position/shape adjustment, these algorithms do not fully follow the least-squares conditions and are accordingly called Quasi-ALS.

In this talk, an application of SFA and WFA will be discussed, using emotional intensity profile data.


References:
Cattell, R. B. (1963). The structuring of change by P-technique and incremental R-technique. In C. W. Harris (Ed.), Problems in measuring change (pp. 167–198). Madison: University of Wisconsin Press.

Harshman, R. A., Hong, S., & Lundy, M. E. (2003). Shifted Factor Analysis—part I: Models and properties. Journal of Chemometrics, 17, 363–378.

Hong, S., Harshman, R. A. (2003). Shifted Factor Analysis—part II: Algorithms. Journal of Chemometrics, 17, 379–388.

Hong, S., Harshman, R. A. (2003). Shifted Factor Analysis—part III: N-way generalization and application. Journal of Chemometrics, 17, 389–399.

Hong, S. (2009). Warped Factor Analysis. Journal of Chemometrics, 23, 371–384.
Date: Tue Dec 8, 12:15 pm - 1:15 pm
Place: room 02.51 (Department of Psychology, Tiensestraat 102, 3000 Leuven)