Geometry-Inference based Clustering Heuristic: A New kmeans initialization technique for Gaussian data and Experimental Proof of concept

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Abstract Kmeans is one of the most algorithms that are utilized in data analysis adopting a variety of different metrics; but kmeans was shown to be sensitive to sensitive to the initialization step. Hence, in this paper, a new Geometry-Inference based Clustering heuristic is proposed for selecting the optimal numbers of clusters for kmeans of in other terms, the algorithm initialization. The conceptual approach proposes the “Initial speed rate” as the main geometric parameter to be statistically analysed. The distributions of this latter are then fitted using classical parametric probability distributions. The resulting fitted parameters show salient 2-stages linear behaviour according to the number of clusters within the kmeans process. Thus, the optimal number of clusters k* was assigned to the intersection of the 2 detected lines for all datasets adopted in this work. The benchmark analysis showed that the proposed heuristic is very competitive compared to other kmeans classical metrics.

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