Simultaneous clustering and variable selection: A novel algorithm and model selection procedure.

The growing availability of high-dimensional data sets offers behavioral scientists an unprecedented opportunity to integrate the information hidden in the novel types of data (e.g., genetic data, social media data, and GPS tracks, etc.,) and thereby obtain a more detailed and comprehensive view towards their research questions. In the context of clustering, analyzing the large volume of variables could potentially result in an accurate estimation or a novel discovery of underlying subgroups. However, a unique challenge is that the high-dimensional data sets likely involve a significant amount of irrelevant variables. These irrelevant variables do not contribute to the separation of clusters and they may mask cluster partitions. The current paper addresses this challenge by introducing a new clustering algorithm, called Cardinality K-means or CKM, and by proposing a novel model selection strategy. CKM is able to perform simultaneous clustering and variable selection with high stability. In two simulation studies and an empirical demonstration with genetic data, CKM consistently outperformed competing methods in terms of recovering cluster partitions and identifying signaling variables. Meanwhile, our novel model selection strategy determines the number of clusters based on a subset of variables that are most likely to be signaling variables. Through a simulation study, this strategy was found to result in a more accurate estimation of the number of clusters compared to the conventional strategy that utilizes the full set of variables. Our proposed CKM algorithm, together with the novel model selection strategy, has been implemented in a freely accessible R package.