Diagnostics for choosing the number of clusters (candidate tones)

Runs k-means across a range of k and reports the elbow (total within-cluster sum of squares), average silhouette width, and – when the cluster / mclust packages are available – the gap statistic and the GMM/BIC-preferred k. No single index is authoritative; use the spread to read off a plausible range for the number of tones.

Usage

choose_k_f0(feat, k_range = 2:8, nstart = 25L, gap = TRUE, bending = 1)

Arguments

feat: A list from cluster_features(), or a numeric feature matrix.
k_range: Integer vector of cluster counts to evaluate. Default 2:8.
nstart: k-means restarts. Default 25.
gap: Whether to compute the gap statistic (needs the cluster package). Default TRUE.
bending: MDL bending factor (>= 1; Kaland & Ellison 2023). Higher values down-weight the model/residual cost so fewer clusters are preferred; tune until the MDL (information-cost) curve is U-shaped. Default 1.

Value

A list with table (k, wss, silhouette, gap, gap_se, mdl), suggestions k_silhouette, k_gap, k_gmm, k_mdl (any may be NA), and assignments (the per-k k-means cluster vectors).

References

Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65.

Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society B, 63(2), 411–423.

Kaland, C., & Ellison, T. M. (2023). Evaluating cluster analysis on f0 contours: An information theoretic approach on three languages. Proceedings of the 20th International Congress of Phonetic Sciences, 3448–3452.