AutoElbow: An Automatic Elbow Detection Method for Estimating the Number of Clusters in a Dataset

Abstract

The elbow technique is a well-known method for estimating the number of clusters required as a starting parameter in the K-means algorithm and certain other unsupervised machine-learning algorithms. However, due to the graphical output nature of the method, human assessment is necessary to determine the location of the elbow and, consequently, the number of data clusters. This article presents a simple method for estimating the elbow point, thus, enabling the K-means algorithm to be readily automated. First, the elbow-based graph is normalized using the graph’s minimum and maximum values along the ordinate and abscissa coordinates. Then, the distance between each point on the graph to the minimum (i.e., the origin) and maximum reference points, and the “heel” of the graph are calculated. The estimated elbow location is, thus, the point that maximizes the ratio of these distances, which corresponds to an approximate number of clusters in the dataset. We demonstrate that the strategy is effective, stable, and adaptable over different types of datasets characterized by small and large clusters, different cluster shapes, high dimensionality, and unbalanced distributions. We provide the clustering community with a description of the method and present comparative results against other well-known methods in the prior state of the art.

Keywords

• automatic
• clustering
• elbow method
• K-means
• unsupervised