A Comparative Evaluation of Different Distance Measures for Determining Initial Seeds in the K-means Algorithm

The selection of a particular distance metric can have a substantial impact on the efficiency of a clustering process and, consequently, the outcome. QuIK, a deterministic seeding method for the K-means algorithm that we previously proposed, uses a unique distance function. With quartiles as the first centers, our unique distance function measures closeness by calculating the minimum absolute difference between each data point and each quartile (Q1, Q2, and Q3), and places each data point in the cluster of the closest quartile. In this paper we show with the help of simulations on both real and artificial datasets, that the unique distance function proposed by us for the QuIK seeding approach beats some of the most popular distance functions in the literature including Euclidean, Manhattan, and Chebyshev, at identifying object similarity in numerical data. The results of our simulations show that our proposed distance measure performs noticeably better than the distance measures used widely in the K-means algorithm, and therefore, our proposed distance metric has the potential to be applied in the K-means algorithm to increase the algorithm’s efficacy.