Reference:
Jaakko Luttinen. Gaussian-process factor analysis for modeling spatio-temporal data. Master's thesis, Helsinki University of Technology, December 2009.
Abstract:
The main theme of this thesis is analyzing and modeling large spatio-temporal datasets, such as global temperature measurements. The task is typically to extract relevant structure and features for predicting or studying the system. This can be a challenging problem because simple models are often not able to capture the complex structure suffiently well, and more sophisticated models can be computationally too expensive in practice.
This thesis presents a novel spatio-temporal model which extends factor analysis by setting Gaussian process priors over the spatial and temporal components. In contrast to factor analysis, the presented model is capable of modeling complex spatial and temporal structure. Compared to standard Gaussian process regression over the spatio-temporal domain, the presented model gains substantial computational savings by operating only in the spatial or temporal domain at a time. Thus, it is feasible to model larger spatio-temporal datasets than with standard Gaussian process regression.
The new model combines the modeling assumptions of several traditional techniques used for analyzing spatially and temporally distributed data: kriging is used for modeling spatial dependencies; empirical orthogonal functions reduce the dimensionality of the problem; and temporal smoothing finds relevant features from time series.
The model is applied to reconstruct missing values in a historical sea surface temperature dataset. The results are promising and suggest that the proposed model may outperform the state-of-the-art reconstruction systems.
Suggested BibTeX entry:
@mastersthesis{Luttinen:2009:MSc,
author = {Jaakko Luttinen},
month = {December},
school = {Helsinki University of Technology},
title = {Gaussian-process factor analysis for modeling spatio-temporal data},
year = {2009},
}
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