Abstract
Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.
Highlights
IntroductionCluster analysis has been widely applied for dividing objects into different groups based on their similarities [2]
There is a high demand for developing new methods to discover hidden structures, identify patterns, and recognize different groups in machine learning applications [1].Cluster analysis has been widely applied for dividing objects into different groups based on their similarities [2]
We showed that the clustering results highly depend on the selected kernel function when using kernel k-means method
Summary
Cluster analysis has been widely applied for dividing objects into different groups based on their similarities [2]. Cluster analysis is an unsupervised learning method [5] to optimize an objective function based on features similarities [6]. Clustering algorithms often use a search method to optimize the objective function. An objective function is optimized by minimizing the distance of elements to their cluster centers (within-cluster distance) and/or maximizing the distance between cluster centers (between-cluster distance). New cluster centers are obtained by averaging the Euclidean distances of all elements grouped in the same cluster in Step 2. K-means objective functions can be written as ∑kK = 1 ∑ xi ∈ πk k xi − μk k2 , where πk is cluster k, μk is the center of cluster k, and k · k is the Euclidean distance
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