The present work extends the application of the recently submitted functional singular spectrum analysis (FSSA) into the realm of structure level subsequence clustering. We begin with a comprehensive review of principal component analysis (PCA), functional principal component analysis (FPCA), singular spectrum analysis (SSA), and the recently submitted FSSA. We computationally show that the novel FSSA-FPCA hybrid clustering technique can be employed as an effective structure-based subsequence clustering method for call-center functional time series data where the method behaves as a dimension reduction technique for time-dependent data. Metrics, such as the F-ratio from k-means clustering, the w-correlation between reconstructed functional time series, and the Rand index are offered to determine the quality of clustering results of labeled functional data. We find that these outcomes are dependent on the grouping stage of FSSA for the call-center data. We also find that our measurements are not significantly sensitive to changes in groupings. Our investigations show that FSSA behaves as a type of temporal to frequency domain transformation similar to that of a Fourier analysis. The results shown in the present essay can be used to extend FSSA in its maturation and offer insight into how the hybrid method should be used and the challenges one faces with it.
Trinka, Jordan, "Functional Singular Spectrum Analysis and the Clustering of Time-Dependent Data" (2019). Mathematics, Statistics and Computer Science Student Research. 1.