Warped image factor analysis

In factor analysis of sequential data (e.g., time-series or digitized images), the measurement sequence remains "intact" and is assumed to be consistent across all measurement conditions. Otherwise, recovered sequential factors would be distorted. Shifted and warped factor analyses (SFA and WFA) explicitly fit such measurement-sequence inconsistency. Warped image factor analysis (WIFA) combines two ideas: (a) fitting systematic shape variation of image factors, and (b) decomposing many 2D images into a few image factors. WIFA allows image factors to change shape independently, unlike what is assumed in a data-level adjustment: synchronized shape changes of image factors. The latent-level shape variation modeled in WIFA seems to make recovered factors "unique" in some two-way cases, as in SFA and WFA. The shape variation of image factors is parameterized as bilinear warping of segmented images. A quasi-ALS (alternating least squares) algorithm for WIFA is described, which uses alternating regression for factor weights and nonlinear optimization for warping-size parameters. The method is demonstrated with a simulated example