Statistical data preprocessing methods in distance functions to enhance k-means clustering algorithm

Clustering is an unsupervised classification method with major aim of partitioning, where objects in the same cluster are similar, and objects belong to different clusters vary significantly, with respect to their attributes. The K-Means algorithm is the commonest and fast technique in partitional cluster algorithms, although with unnormalized datasets it can achieve local optimal. We introduced two new approaches to normalization techniques to enhance the K-Means algorithms. This is to remedy the problem of using the existing Min-Max (MM) and Decimal Scaling (DS) techniques, which have overflow weakness. The suggested approaches are called new approach to min-max (NAMM) and decimal scaling (NADS). The Hybrid mean algorithms which are based on spherical clusters is also proposed to remedy the most significant limitation of the K-Means and K-Midranges algorithms. It is attained successfully by combining the mean in K-Means algorithm, minimum and maximum in K-Midranges algorithm and compute their average as mean cluster of Hybrid mean. The problem of using range function in Heterogeneous Euclidean-Overlap Metric (HEOM) is addressed by replacing the range with interquartile range function called Interquartile Range-Heterogeneous Metric (IQR-HEOM). Dividing the HEOM with range allows outliers to have big effect on the contribution of attributes. Hence, We proposed interquartile range which is more resistance against outliers in data pre-processing. It shows that the IQR-HEOM method is more efficient to rectify the problem caused by using range in HEOM. The Standardized Euclidean distance which uses standard deviation to down weight maximum points of the ith features on the distance clusters are being criticized in the literature by many researchers that the method is prone to outliers and has 0% breakdown points. Therefore, to remedy the problem, we introduced two statistical estimators called Qn and Sn estimator, both have 50% breakdown points, with their efficiency as 58% and 82% for Sn and Qn, respectively. The empirical evidences show that the two suggested methods are more efficient compared to the existing methods.

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