text: This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods to yield a density-based hierarchical clustering algorithm. Our investigation begins with formally defining the types of clusters DP and DBSCAN are designed to detect; and then identifies the kinds of distributions that DP and DBSCAN individually fail to detect all clusters in a dataset. These identified weaknesses inspire us to formally define a new kind of clusters and propose a new method called DC-HDP to overcome these weaknesses to identify clusters with arbitrary shapes and varied densities. In addition, the new method produces a richer clustering result in terms of hierarchy or dendrogram for better cluster structures understanding. Our empirical evaluation results show that DC-HDP produces the best clustering results on 14 datasets in comparison with 7 state-of-the-art clustering algorithms.
  @cite_21: Cluster analysis is a primary method for database mining. It is either used as a stand-alone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many real-data sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure. This cluster-ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only 'traditional' clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the cluster-ordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.
summary: Many variants of DBSCAN have been attempted to overcome the weakness of detecting clusters with varied densities. OPTICS @cite_21 draws a reachability'' plot based on the @math -nearest neighbour distance. In the @math -axis of the plot, adjacent points follow close to each other such that point @math is the closest to @math in terms of the reachability distance'' The reachability-distance'' of object @math to object @math is the greater one between the core distance'' of @math and the distance between @math and @math . The core distance'' of @math is the minimum @math that makes @math a core'' object (the distance to its @math -nearest neighbour, @math ). . The reachability distance for each point is shown in @math -axis. Since clusters centre normally has a higher density or lower reachability distance than the cluster boundaries, each cluster is visible as a valley'' in this plot. Then a hierarchical method can be used to extract different clusters. The overall clustering performance depends on the hierarchical method employed on the reachability plot.