Clustering algorithms based on volume criteria

Clustering algorithms such as the K-means algorithm and the fuzzy C-means algorithm are based on the minimization of the trace of the (fuzzy) within-fluster scatter matrix. In this paper, we explore the use of determinant (volume) criteria for clustering. We derive an algorithm called the minimum scatter volume (MSV) algorithm, that minimizes the scatter volume, and another algorithm called the minimum cluster volume (MCV) that minimizes the sum of the volumes of the individual clusters. The behavior of MSV is shown to be similar to that of K-means, whereas MCV is more versatile