Array Independent Component Analysis with Application to Remote Sensing

of the Dissertation Array Independent Component Analysis with Application to Remote Sensing by Irina A. Kukuyeva Doctor of Philosophy in Statistics University of California, Los Angeles, 2012 Professor Jan de Leeuw, Chair There are three ways to learn about an object: from samples taken directly from the site, from simulation studies based on its known scientific properties, or from remote sensing images [64]. All three are carried out to study Earth and Mars. Our goal, however, is to learn about the second largest storm on Jupiter, called the White Oval, whose characteristics are unknown to this day [55]. As Jupiter is a gas giant and hundreds of millions of miles away from Earth [13], we can only make inferences about about the planet from retrieval algorithms and remotely sensed images. Our focus is to find latent variables from the remotely sensed data that best explain its underlying atmospheric structure. Principal Component Analysis (PCA) is currently the most commonly employed technique to do so. For a data set with more than two modes, this approach fails to account for all of the variable interactions, especially if the distribution of the variables is not multivariate normal; an assumption that is rarely true of multispectral images. The thesis presents an overview of PCA along with the most commonly employed decompositions in other fields: Independent Component Analysis, Tucker-3 and CANDECOMP/PARAFAC and discusses their limitations in finding unobserved, independent structures in a data cube.