A study on sparse k-means clustering for histogram-valued data

In this paper, we investigate a sparse k-means clustering method for histogram-valued data. The distances between histogram-valued observations are defined using the Wasserstein-Kantorovich distances to group p-dimensional histogram-valued data. Clustering is performed using the sparse k-means clustering method with the distance matrix computed for each dimension. The proposed method maximizes the weighted sums of squared distances between clusters. For various value of k, we apply the sparse k-means clustering method and determine the optimal number of clusters with the Silhouette measure. Simulation studies were conducted to compare the proposed method with the standard k-means clustering method in terms of cluster agreement and selected variables. Additionally, we analyzed real data from the monthly average temperatures of 48 US states. As a result of numerical analysis, it was confirmed that the proposed method shows superior performance and effective variable selection.