Abstract
Fuzzy clustering is a clustering method whcih allows an object to belong to two or more cluster by combining hard-clustering and fuzzy membership matrix. Two popular algorithms used in fuzzy clustering are Fuzzy C-Means (FCM) and Gustafson Kessel (GK). The FCM use Euclideans distance for determining cluster membership, while GK use Fuzzy Covariance Matrix that considering covariance between variables. Although GK perform better, it has some drawbacks on handling linearly correlated data, and as FCM the algorithm produce unstable result due to random initialization. These drawbacks can be overcame by using improved covariance estimation and cluster ensemble, respectively. This research presents the implementation of improved covariance estimation and cluster ensemble on GK method and compare it with FCM-Ensemble.
Highlights
Clustering is data exploration method for obtaining the hidden characteristics on data by forming groups without any prior information in the form of labels and grouping mechanism [1]
For the Fuzzy C-Means (FCM) we use the Euclidean distance (Eq 4), while GK use the distance function defined in Eq
The Xie Beni (XB) index calculated by using that parameters on FCM-Ensemble is 0.067203
Summary
Clustering is data exploration method for obtaining the hidden characteristics on data by forming groups without any prior information in the form of labels and grouping mechanism [1]. The conventional hard clustering method, such as K-Means, restricts that each observation become a member to exactly one cluster. It cannot provide a proper result when data have the same distance to other cluster center (centroid) or are in a boundary group. The euclidean distance is a simple and popular technique but have disadvantage that only perform best on well-separated cluster (no overlapping cluster boundary) and each cluster have spherical shape. This weakness is overcome by the GK by using fuzzy covariance matrix that represent both ellipsoidal
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