Array Independent Component Analysis with Application to Remote Sensing

Irina A Kukuyeva
Ph.D., 2012
Advisor: Jan de Leeuw

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.

We motivate the need for a novel dimension reduction technique that generalizes existing decompositions to find latent, statistically independent variables for one side of a multimodal (number of modes greater than two) data set while accounting for the variable interactions with its other modes. Our method is called Array Independent Component Analysis (AICA). As the main question of any decomposition is how to select a small number of latent variables that best capture the structure in the data, we extend the heuristic developed by Ceulemans and Kiers in [10] to aid in model selection for the AICA framework.

The effectiveness of each dimension reduction technique is determined by the degree of interpretability of the uncovered hidden variables. AICA discovered two temperature gradients of the White Oval that matched the ones above the visible clouds of the Great Red Spot (in the North-South and West-East directions) [26], isolated the small storm to the South-East of the White Oval and identified the Raleigh scatter of gas molecules [52]. The other techniques, including PCA, did not isolate these or any other interpretable components.