datanugget:Create, and Refine Data Nuggets

Creating, and refining data nuggets. Data nuggets reduce a large dataset into a small collection of nuggets of data, each containing a center (location), weight (importance), and scale (variability) parameter. Data nugget centers are created by choosing observations in the dataset which are as equally spaced apart as possible. Data nugget weights are created by counting the number observations closest to a given data nugget center. We then say the data nugget 'contains' these observations and the data nugget center is recalculated as the mean of these observations. Data nugget scales are created by calculating the trace of the covariance matrix of the observations contained within a data nugget divided by the dimension of the dataset. Data nuggets are refined by 'splitting' data nuggets which have scales or shapes (defined as the ratio of the two largest eigenvalues of the covariance matrix of the observations contained within the data nugget) Reference paper: [1] Beavers, T. E., Cheng, G., Duan, Y., Cabrera, J., Lubomirski, M., Amaratunga, D., & Teigler, J. E. (2024). Data Nuggets: A Method for Reducing Big Data While Preserving Data Structure. Journal of Computational and Graphical Statistics, 1-21. [2] Cherasia, K. E., Cabrera, J., Fernholz, L. T., & Fernholz, R. (2022). Data Nuggets in Supervised Learning. \emph{In Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler} (pp. 429-449). Cham: Springer International Publishing.