Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are assumed to be separated by relatively sparse regions. The samples are eroded sequentially according to their dynamic boundary densities. The erosion starts from low density regions, invading inwards, until all the samples are eroded out. By this manner, boundaries between different clusters become more and more apparent. It therefore offers a natural and powerful way to separate the clusters when the boundaries between them are hard to be drawn at once. With the sequential order of being eroded, the sequential boundary levels are produced, following which the clusters in arbitrary shapes are automatically reconstructed. As demonstrated across various clustering tasks, it is able to outperform most of the state-of-the-art algorithms and its performance is nearly perfect in some scenarios.
. . Function @math in Eqn. returns the distance between @math and @math . In the second step, the clusters are forged basically in two different manners. For instance, in DBSCAN @cite_1 , cluster is formed by expanding it from core points'' (points hold high density) to points with low density. While in mean-shift clustering @cite_26 , data samples are shifted iteratively from region of low density towards the density peaks. In DBSCAN, the expansion process could be very sensitive to the parameters. For instance, two heterogeneous clusters are falsely merged into one as the parameter changes slightly. While in mean-shift, the shifting process could be easily stuck in a local if there is no obvious density peak. In the approach of clustering based on density peak (clusterDP) @cite_32 , data samples are directly assigned to the closest density peak in which each density peak is recognized as a cluster center. However, it faces similar problem as mean-shift since it is hard to identify the cluster center when there is no obvious density peak. Another pitfall of this approach is that the number of peaks to be selected as the cluster center has to be set manually.
@cite_26 @cite_1 @cite_32
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Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on the surface constructed with a "shadow" kernal. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. > Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover clusters of arbitrary shape. DBSCAN requires only one input parameter and supports the user in determining an appropriate value for it. We performed an experimental evaluation of the effectiveness and efficiency of DBSCAN using synthetic data and real data of the SEQUOIA 2000 benchmark. The results of our experiments demonstrate that (1) DBSCAN is significantly more effective in discovering clusters of arbitrary shape than the well-known algorithm CLARANS, and that (2) DBSCAN outperforms CLARANS by a factor of more than 100 in terms of efficiency. Given a large collection of unlabeled face images, we address the problem of clustering faces into an unknown number of identities. This problem is of interest in social media, law enforcement, and other applications, where the number of faces can be of the order of hundreds of million, while the number of identities (clusters) can range from a few thousand to millions. To address the challenges of run-time complexity and cluster quality, we present an approximate Rank-Order clustering algorithm that performs better than popular clustering algorithms (k-Means and Spectral). Our experiments include clustering up to 123 million face images into over 10 million clusters. Clustering results are analyzed in terms of external (known face labels) and internal (unknown face labels) quality measures, and run-time. Our algorithm achieves an F-measure of 0.87 on the LFW benchmark (13 K faces of 5,749 individuals), which drops to 0.27 on the largest dataset considered (13 K faces in LFW + 123M distractor images). Additionally, we show that frames in the YouTube benchmark can be clustered with an F-measure of 0.71. An internal per-cluster quality measure is developed to rank individual clusters for manual exploration of high quality clusters that are compact and isolated.