Abstract
The k-means algorithm is sensitive to the outliers. In this paper, we propose a robust two-stage k-means clustering algorithm based on the observation point mechanism, which can accurately discover the cluster centers without the disturbance of outliers. In the first stage, a small subset of the original data set is selected based on a set of nondegenerate observation points. The subset is a good representation of the original data set because it only contains all those points that have a higher density of the original data set and does not include the outliers. In the second stage, we use the k-means clustering algorithm to cluster the selected subset and find the proper cluster centers as the true cluster centers of the original data set. Based on these cluster centers, the rest data points of the original data set are assigned to the clusters whose centers are the closest to the data points. The theoretical analysis and experimental results show that the proposed clustering algorithm has the lower computational complexity and better robustness in comparison with k-means clustering algorithm, thus demonstrating the feasibility and effectiveness of our proposed clustering algorithm.
Highlights
Clustering is an important research branch of data mining. e k-means algorithm is one of the most popular clustering methods [1]
We have conducted a series of experiments on 6 synthetic data sets and 3 benchmark data sets (UCI [22] and KEEL [23]) to validate the effectiveness of the proposed two-stage k-means clustering algorithm . e synthetic data sets can be downloaded from BaiduPan with the extraction code “p3mc.”
, respectively. ere are two outliers in data set #1. We choose another four synthetic data sets as shown in Figure 3 and three real-world data sets to compare the clustering performances of our proposed algorithm with the kmeans algorithm. e details of these data sets and experimental results are summarized in Table 1, where N is the number of the elements of the data set, t is the proportion of the outlier in the data set, k is the number of clusters, d is the dimension of data point, p is the percentile number, nc is the cardinality of selected subset, ARIkmeans and Timekmeans are the adjusted Rand index (ARI) and time consumption of k-means algorithm, and ARIour and Timeour are ARI and time consumption of our proposed algorithm
Summary
We propose a robust two-stage k-means clustering algorithm based on the observation point mechanism, which can accurately discover the cluster centers without the disturbance of outliers. A small subset of the original data set is selected based on a set of nondegenerate observation points. We use the k-means clustering algorithm to cluster the selected subset and find the proper cluster centers as the true cluster centers of the original data set. Based on these cluster centers, the rest data points of the original data set are assigned to the clusters whose centers are the closest to the data points. Based on these cluster centers, the rest data points of the original data set are assigned to the clusters whose centers are the closest to the data points. e theoretical analysis and experimental results show that the proposed clustering algorithm has the lower computational complexity and better robustness in comparison with k-means clustering algorithm, demonstrating the feasibility and effectiveness of our proposed clustering algorithm
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