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What are some examples of applying spectral clustering to financial times series data or other areas of finance? Why spectral clustering was used for each application rather than other types of clustering would help too.

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One spectral analysis technique involves decomposing a univariate time series using SVD, assigning eigenvectors to two or more groups with k-means or another clustering algorithm, with the least significant group discarded as noise and the remaining groups used for reconstruction.

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You are kindly advised to take a look at Chapter 9 of "Big Data Science in Finance" by Aldridge and Avellaneda

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