The Annals of Applied Statistics

Functional factor analysis for periodic remote sensing data

Chong Liu, Surajit Ray, Giles Hooker, and Mark Friedl

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Abstract

We present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components that are nearly-periodic and nearly-aperiodic with a predefined period. We show that the factor rotation can be obtained by calculation of canonical correlations between appropriate spaces which make the methodology computationally efficient. Moreover, we demonstrate that our proposed rotations provide stable and interpretable results in the presence of highly complex covariance. This work is motivated by the goal of finding interpretable sources of variability in gridded time series of vegetation index measurements obtained from remote sensing, and we demonstrate our methodology through an application of factor rotation of this data.

Article information

Source
Ann. Appl. Stat. Volume 6, Number 2 (2012), 601-624.

Dates
First available: 11 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1339419609

Digital Object Identifier
doi:10.1214/11-AOAS518

Zentralblatt MATH identifier
06062732

Mathematical Reviews number (MathSciNet)
MR2976484

Citation

Liu, Chong; Ray, Surajit; Hooker, Giles; Friedl, Mark. Functional factor analysis for periodic remote sensing data. The Annals of Applied Statistics 6 (2012), no. 2, 601--624. doi:10.1214/11-AOAS518. http://projecteuclid.org/euclid.aoas/1339419609.


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Supplemental materials

  • Supplementary material: Description of data and details of simulation. The supplementary material is divided into 3 sections. The first section provides a detailed description of the Harvard Forest data that is used in this article, including preprocessing steps. We also provide a detailed description of the imputation steps for pixels with missing observations. The second section provides a description of Annual Information and its application is demonstrated through a simulation study. The last section provides results related to the bootstrap hypothesis testing procedure proposed in this article. In particular, we present the test results on the Harvard Forest data and simulation studies where we explore the empirical power curve and size on simulated data sets.