Rosse, Patrick J., authorKirby, Michael, advisorPeterson, Chris, committee memberAdams, Henry, committee memberAnderson, Chuck, committee member2020-09-072020-09-072020https://hdl.handle.net/10217/212016With "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.born digitalmasters thesesengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.EigenmapsLaplaciantime seriesembeddingdimensional reductionoptimizationText