Functional clustering of fictional narratives using Vonnegut curves

Motivated by a public suggestion by the famous novelist Kurt Vonnegut, we clustered functional data that represented sentiment curves for famous fictional stories. We analyzed text data from novels written between 1612 and 1925, and transformed them into curves measuring sentiment as a function of the percentage of elapsed contents of the novel. We employed sentence-level sentiment evaluation and nonparametric curve smoothing. Our clustering methods involved finding the optimal number of clusters, aligning curves using different chronological warping functions to account for phase and amplitude variation, and implementing functional K-means algorithms under the square root velocity framework. Our results revealed insights about patterns in fictional narratives that Vonnegut and others have suggested but not analyzed in a functional way.