Author

Jon Devine

Date of Award

8-2009

Level of Access

Open-Access Thesis

Degree Name

Master of Science (MS)

Department

Spatial Information Science and Engineering

Advisor

M. Kate Beard-Tisdale

Second Committee Member

Tony Stefanidis

Third Committee Member

Silvia Nittel

Abstract

Phenomena occur both in space and time. Correspondingly, ability to model spatiotemporal behavior translates into ability to model phenomena as they occur in reality. Given the complexity inherent when integrating spatial and temporal dimensions, however, the establishment of computational methods for spatiotemporal analysis has proven relatively elusive. Nonetheless, one method, the spatiotemporal helix, has emerged from the field of video processing. Designed to efficiently summarize and query the deformation and movement of spatiotemporal events, the spatiotemporal helix has been demonstrated as capable of describing and differentiating the evolution of hurricanes from sequences of images. Being derived from image data, the representations of events for which the spatiotemporal helix was originally created appear in areal form (e.g., a hurricane covering several square miles is represented by groups of pixels). ii Many sources of spatiotemporal data, however, are not in areal form and instead appear as points. Examples of spatiotemporal point data include those from an epidemiologist recording the time and location of cases of disease and environmental observations collected by a geosensor at the point of its location. As points, these data cannot be directly incorporated into the spatiotemporal helix for analysis. However, with the analytic potential for clouds of point data limited, phenomena represented by point data are often described in terms of events. Defined as change units localized in space and time, the concept of events allows for analysis at multiple levels. For instance lower-level events refer to occurrences of interest described by single data streams at point locations (e.g., an individual case of a certain disease or a significant change in chemical concentration in the environment) while higher-level events describe occurrences of interest derived from aggregations of lower-level events and are frequently described in areal form (e.g., a disease cluster or a pollution cloud). Considering that these higher-level events appear in areal form, they could potentially be incorporated into the spatiotemporal helix. With deformation being an important element of spatiotemporal analysis, however, at the crux of a process for spatiotemporal analysis based on point data would be accurate translation of lower-level event points into representations of higher-level areal events. A limitation of current techniques for the derivation of higher-level events is that they imply bias a priori regarding the shape of higher-level events (e.g., elliptical, convex, linear) which could limit the description of the deformation of higher-level events over time. The objective of this research is to propose two newly developed kernel methods, support vector clustering (SVC) and support vector machines (SVMs), as means for iii translating lower-level event points into higher-level event areas that follow the distribution of lower-level points. SVC is suggested for the derivation of higher-level events arising in point process data while SVMs are explored for their potential with scalar field data (i.e., spatially continuous real-valued data). Developed in the field of machine learning to solve complex non-linear problems, both of these methods are capable of producing highly non-linear representations of higher-level events that may be more suitable than existing methods for spatiotemporal analysis of deformation. To introduce these methods, this thesis is organized so that a context for these methods is first established through a description of existing techniques. This discussion leads to a technical explanation of the mechanics of SVC and SVMs and to the implementation of each of the kernel methods on simulated datasets. Results from these simulations inform discussion regarding the application potential of SVC and SVMs.

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