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Anomaly Detection with Advanced Nonlinear Dimensionality Reduction

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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.

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  • etd-3696
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  • 2020
Date created
  • 2020-05-07
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  • 2021-02-01

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Permanent link to this page: https://digital.wpi.edu/show/pv63g2831