Generalized Reduced K–Means

In the context of sports analytics, the evaluation of players’ performance has traditionally been a complex endeavor, given the multidimensional nature of the data involved. This paper introduces a novel approach for multivariate analyses of complex data sets, with a focus on professional basketball data. The proposed model simultaneously performs unsupervised classification of units into K clusters and their optimal low-dimensional reconstruction. This is done considering variables’ dimensionality representation into Q components for each group of clusters that can be identified by the same latent dimensions. Consequently, we refer to the new model as Generalized Reduced K-Means (GRKM), which includes RKM as a special case when a unique lower rank reconstruction of the variables is needed. Before the application on real data, the effectiveness of the proposal is shown by means of an extended simulation study. By applying this innovative method to a comprehensive set of National Basketball Association (NBA) statistics, we demonstrate its efficacy in distinguishing player profiles across offensive and defensive spectrums, simultaneously grouping them into coherent clusters.