Laplacian Eigenmaps for time series analysis
Date
2020
Authors
Rosse, Patrick J., author
Kirby, Michael, advisor
Peterson, Chris, committee member
Adams, Henry, committee member
Anderson, Chuck, committee member
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Abstract
With "Big Data" becoming more available in our day-to-day lives, it becomes necessary to make meaning of it. We seek to understand the structure of high-dimensional data that we are unable to easily plot. What shape is it? What points are "related" to each other? The primary goal is to simplify our understanding of the data both numerically and visually. First introduced by M. Belkin, and P. Niyogi in 2002, Laplacian Eigenmaps (LE) is a non-linear dimensional reduction tool that relies on the basic assumption that the raw data lies in a low-dimensional manifold in a high-dimensional space. Once constructed, the graph Laplacian is used to compute a low-dimensional representation of the data set that optimally preserves local neighborhood information. In this thesis, we present a detailed analysis of the method, the optimization problem it solves, and we put it to work on various time series data sets. We show that we are able to extract neighborhood features from a collection of time series, which allows us to cluster specific time series based on noticeable signatures within the raw data.
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Subject
Eigenmaps
Laplacian
time series
embedding
dimensional reduction
optimization