Understanding the Interplay Between Metrics, Normalization Forms, and Data distribution in K-Means Clustering: A Comparative Simulation Study

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

“…Similar studies were performed regarding the simple-effect of the normalization by number of researches such as [27] and [28], and other were dedicated to the simple effect of the clusters' shapes such as Kłopotek et al 2020 which proved kmeans clusters should be hyper(ball)-shaped ones to converge to the global optimum [25], similar statement was proposed by Qiu 2010 [29]. The results of Kłopotek et al 2020 [25] are in total concordance with those of El Khattabi et al 2022 [26] since it was found that normal (Gaussian) standardization are well adapted to Gaussian data-shapes, named in the EL Khattabi's paper as Likely-Gaussian datasets, and in Kłopotek's paper as hyper(ball)-shaped data. Similarly, Hennig 2022 studied nine clustering methods by means of several cluster validation indexes [30], The author measured various individual aspects of the data sets such the scales of data, the clusters separation criterion, and the datasets shapes as mainly the closeness to spatial Gaussian distribution, and so forth.…”

“…In a previous work, the authors of the present paper experimentally proved the importance of data preparation in terms of normalization, and the importance of the data dispersion which was qualified as space data shape, then, these two characteristics were combined with different kmeans metrics for a series of datasets. The findings clearly showed the tri-fold interplay between the latter parameters but also the important sensitivity of these latter on the clustering results [26]. Similar studies were performed regarding the simple-effect of the normalization by number of researches such as [27] and [28], and other were dedicated to the simple effect of the clusters' shapes such as Kłopotek et al 2020 which proved kmeans clusters should be hyper(ball)-shaped ones to converge to the global optimum [25], similar statement was proposed by Qiu 2010 [29].…”

“…A preliminary analysis showed worst quality of results regarding the min-max normalisation. Hence, this is only the standardized normalization of equation ( 2) which was maintained in this work as it was proved by [25] and [26] especially for Gaussian datasets.…”

“…The study of these subsets should reveal the interest of the proposed algorithm and its ability to catch accurate and reliable information for both higher and lower clusters counts. Moreover, it is worth pointing out that datasets should be normalized before starting any operation or computing as it was earlier demonstrated by the authors in a previous publication [26]. Hence, additionally to the row data analysis, two normalization techniques, Equations (1) and (2), were considered in [26].…”

“…Moreover, it is worth pointing out that datasets should be normalized before starting any operation or computing as it was earlier demonstrated by the authors in a previous publication [26]. Hence, additionally to the row data analysis, two normalization techniques, Equations (1) and (2), were considered in [26].…”