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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Computer Science
Year Degree Awarded
2017
Month Degree Awarded
September
First Advisor
Sridhar Mahadevan
Second Advisor
Don Towsley
Third Advisor
Ben Marlin
Fourth Advisor
Darby Dyar
Subject Categories
Artificial Intelligence and Robotics
Abstract
Manifold learning is a class of machine learning methods that exploits the observation that high-dimensional data tend to lie on a smooth lower-dimensional manifold. Manifold discovery is the essential first component of manifold learning methods, in which the manifold structure is inferred from available data. This task is typically posed as a graph construction problem: selecting a set of vertices and edges that most closely approximates the true underlying manifold. The quality of this learned graph is critical to the overall accuracy of the manifold learning method. Thus, it is essential to develop accurate, efficient, and reliable algorithms for constructing manifold approximation graphs. To aid in this investigation of graph construction methods, we propose new methods for evaluating graph quality. These quality measures act as a proxy for ground-truth manifold approximation error and are applicable even when prior information about the dataset is limited. We then develop an incremental update scheme for some quality measures, demonstrating their usefulness for efficient parameter tuning. We then propose two novel methods for graph construction, the Manifold Spanning Graph and the Mutual Neighbors Graph algorithms. Each method leverages assumptions about the structure of both the input data and the subsequent manifold learning task. The algorithms are experimentally validated against state of the art graph construction techniques on a multi-disciplinary set of application domains, including image classification, directional audio prediction, and spectroscopic analysis. The final contribution of the thesis is a method for aligning sequential datasets while still respecting each set’s internal manifold structure. The use of high quality manifold approximation graphs enables accurate alignments with few ground-truth correspondences.
DOI
https://doi.org/10.7275/10605896.0
Recommended Citation
Carey, CJ, "Graph Construction for Manifold Discovery" (2017). Doctoral Dissertations. 1053.
https://doi.org/10.7275/10605896.0
https://scholarworks.umass.edu/dissertations_2/1053