A Distance Metric for Uneven Clusters of Unsupervised K-Means Clustering Algorithm

In this paper, we propose a new distance metric for the K-means clustering algorithm. Applying this metric in clustering a dataset, forms unequal clusters. This metric leads to a larger size for a cluster with a centroid away from the origin, rather than a cluster closer to the origin. The proposed metric is based on the Canberra distances and it is useful for cases that require unequal size clusters. This metric can be used in connected autonomous vehicle wireless networks to classify mobile users such as pedestrians, cyclists, and vehicles. We use a combination of mathematical and exhaustive search to establish its validity as a true distance metric. We compare the K-Means algorithm using the proposed distance metric with five other distance metrics for comparison. These metrics include the Euclidean, Manhattan, Canberra, Chi-squared, and Clark distances. Simulation results depict the effectiveness of our proposed metric compared with the other distance metrics in both one-dimensional and two-dimensional randomly generated datasets. In this paper, we use three internal evaluation measures namely the Compactness, Sum of Squared Errors (SSE), and Silhouette measures. These measures are used to study the proper number of clusters for each of the K-Means algorithms and also select the best run among multiple centroid initializations. The elbow method and the local maximum approach are used alongside the evaluation measures to select the optimal number of clusters.