On the strengths of the self-updating process clustering algorithm

Abstract

The Self-Updating Process (SUP) is a clustering algorithm that stands from the viewpoint of data points and simulates the process how data points move and perform self-clustering. It is an iterative process on the sample space and allows for both time-varying and time-invariant operators. By simulations and comparisons, this paper shows that SUP is particularly competitive in clustering (i) data with noise, (ii) data with a large number of clusters, and (iii) unbalanced data. When noise is present in the data, SUP is able to isolate the noise data points while performing clustering simultaneously. The property of the local updating enables SUP to handle data with a large number of clusters and data of various structures. In this paper, we showed that the blurring mean-shift is a static SUP. Therefore our discussions on the strengths of SUP also apply to the blurring mean-shift. Journal of Statistical Computation and Simulation sup˙arxiv has been implemented in the Generalized Association Plots [13,14]. Compared with the iteratively generated correlation matrices, the self-updating process operates on the sample space, not on the correlation space. It shows the actual movements of data points around the sample space. Data points continue updating their positions until the whole system reaches a balanced therefore static condition, in which the clusters are formed. It is as if the process describes how data points perform self-clustering. We therefore named it Self-Updating Process (SUP).A similar iterative process that also operates on the sample space is the mean-shift algorithm [15]. It has non-blurring and blurring approaches. Compared with the selfupdating process in which operators can be time-varying, both non-blurring and blurring approaches use time-invariant operators. Specific differences between the mean-shift and and the self-updating process are outlined in Section 2.6. The mean-shift algorithm made its first appearance for kernel density estimation by taking the sample mean within a local region to estimate the gradient of a density function. It was further extended and analyzed by Cheng [16]. Comaniciu successfully applied the non-blurring mean-shift algorithm to the problem of image segmentation [17]. Since then the mean-shift algorithm has become well-known in the Computer Science community but not as familiar to the Statistics community. As the implementation of the mean-shift algorithm requires a choice of the kernel function, the Gaussian kernel is very often used in practice [17][18][19]. There are other clustering algorithms that can be viewed as some version of the mean-shift algorithm. For example, Cheng [16] showed that the k-means algorithm is some limit of the non-blurring mean-shift algorithm. Yang and Wu used a total similarity objective function to derive a similarity-based clustering method (SCM) [20], which is a non-blurring mean-shift type clustering algorithm. Although the non-blurring mean-shift is more popular in image processing, Chen et al. [21] reported that the blurring proc...

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“…The overall complexity can thus be reduced to O ( N log( N )) or even O ( N ). Secondly, we incorporated dynamic-SUP [61] into the new clustering algorithm so as to let the number of neighbors grow with iteration. This approach, which allowed us to focus on the local structure at the beginning, indeed gave a better performance in practice.…”