Advances in self-organizing maps for spatiotemporal and nonlinear systems

Abstract

Innovative methods for the extraction of relevant features from water-related data sets will lead to better support of water resources management at local, regional and global scales. The simplification and organisation of the immense amount of multivariate hydrologic data gathered globally is essential to allow patterns to be recognized and useful information to be extracted for easy incorporation into decision-making processes. This thesis introduces specific developments to the self-organizing map method to provide an enhanced extraction and visualization of information from large, high-dimensional hydrological data sets to reveal patterns and clusters that are an accurate representation of the system that produced the data. The self-organizing map is an artificial neural network proficient at extracting and ordering prevalent patterns in a data set, sorting the data in accordance with these patterns and conveying the information through meaningful mappings into low dimensional space. The SOM is a widely used method in water-related research due to its intuitive implementation, resilience to missing and noisy data, ability to integrate real-time data, and straightforward visual summary of the system and intercomponent relationships. Data describing the relationships of human populations with their freshwater resources generally contain difficult-to-define dynamic relationships and vastly differing data sources and measurement techniques, making them especially well-suited for analysis with the SOM. Although most hydrological and water resource systems include a spatiotemporal component (a cross-sectional structure as well as a temporal one) and many also contain nonlinear manifolds (such as fluctuating intervariable relationships generated from diurnal or season effects), the SOM method currently encounters various limitations when applied to spatiotemporal and nonlinear data. In consideration of the current state of SOM knowledge and water-related applications, this thesis is focused on advances to the SOM method through a series of improvements in: the representation of dynamic spatiotemporal data; a method for deliberate, application-specific parameter selection; pattern extraction from highly nonlinear data; and the visualisation of individual pathways of data items though temporal shifts in the cross-sectional structure of the data. Five papers are presented, each concentrating on a distinct aspect of these improvements. Each new development is demonstrated on a real-world, water-related data set.