Faculty Advisor or Committee Member
Randy C. Paffenroth, Advisor
Dimensionality reduction techniques such as t-SNE and UMAP are useful both for overview of high-dimensional datasets and as part of a machine learning pipeline. These techniques create a non-parametric model of the manifold by fitting a density kernel about each data point using the distances to its k-nearest neighbors. In dense regions, this approach works well, but in sparse regions, it tends to draw unrelated points into the nearest cluster. Our work focuses on a homotopy method which imposes graph-based regularization over the manifold parameters to update the embedding. As the homotopy parameter increases, so does the cost of modeling different scales between adjacent neighborhoods. This gradually imposes a more uniform scale over the manifold, resulting in a more faithful embedding which preserves structure in dense areas while pushing sparse anomalous points outward.
Worcester Polytechnic Institute
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Beach, David J., "Anomaly Detection with Advanced Nonlinear Dimensionality Reduction" (2020). Masters Theses (All Theses, All Years). 1378.
Dimensionality Reduction, Anomaly Detection, Manifold Learning, Unsupervised Learning