Clustering Expressive Timing with Regressed Polynomial Coefficients Demonstrated by a Model Selection Test

Though many past works have tried to cluster expressive timing within a phrase, there have been few attempts to cluster features of expressive timing with constant dimensions regardless of phrase lengths. For example, used as a way to represent expressive timing, tempo curves can be regressed by a polynomial function such that the number of regressed polynomial coefficients remains constant with a given order regardless of phrase lengths. In this paper, clustering the regressed polynomial coefficients is proposed for expressive timing analysis. A model selection test is presented to compare Gaussian Mixture Models (GMMs) fitting regressed polynomial coefficients and fitting expressive timing directly. As there are no expected results of clustering expressive timing, the proposed method is demonstrated by how well the expressive timing are approximated by the centroids of GMMs. The results show that GMMs fitting the regressed polynomial coefficients outperform GMMs fitting expressive timing directly. This conclusion suggests that it is possible to use regressed polynomial coefficients to represent expressive timing within a phrase and cluster expressive timing within phrases of different lengths.