Density-based clustering techniques are used in a wide range of data mining applications. One of their most attractive features con- sists in not making use of prior knowledge of the number of clusters that a dataset contains along with their shape. In this paper we propose a new algorithm named Linear DBSCAN (Lin-DBSCAN), a simple approach to clustering inspired by the density model introduced with the well known algorithm DBSCAN. Designed to minimize the computational cost of density based clustering on geospatial data, Lin-DBSCAN features a linear time complexity that makes it suitable for real-time applications on low-resource devices. Lin-DBSCAN uses a discrete version of the density model of DBSCAN that takes ad- vantage of a grid-based scan and merge approach. The name of the algorithm stems exactly from its main features outlined above. The algorithm was tested with well known data sets. Experimental results prove the efficiency and the validity of this approach over DBSCAN in the context of spatial data clustering, enabling the use of a density-based clustering technique on large datasets with low computational cost.
OPTICS (Ordering Points To Identify the Clustering Structure) @cite_34 is a hybrid approach that exhibits features common to both the density and hierarchical clustering paradigms. The output is a special kind of dendrogram of the elements of the dataset, called . All the elements that fall into valleys of the plot belong to the same cluster.
@cite_34
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We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. This paper presents a new approach to hierarchical clustering of point patterns. Two algorithms for hierarchical location- and density-based clustering are developed. Each method groups points such that maximum intracluster similarity and intercluster dissimilarity are achieved for point locations or point separations. Performance of the clustering methods is compared with four other methods. The approach is applied to a two-step texture analysis, where points represent centroid and average color of the regions in image segmentation. Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset. Ensemble clustering, as an important extension of the clustering problem, refers to the problem of combining different (input) clusterings of a given dataset to generate a final (consensus) clustering that is a better fit in some sense than existing clusterings. Over the past few years, many ensemble clustering approaches have been developed. However, most of them are designed for partitional clustering methods, and few research efforts have been reported for ensemble hierarchical clustering methods. In this article, a hierarchical ensemble clustering framework that can naturally combine both partitional clustering and hierarchical clustering results is proposed. In addition, a novel method for learning the ultra-metric distance from the aggregated distance matrices and generating final hierarchical clustering with enhanced cluster separation is developed based on the ultra-metric distance for hierarchical clustering. We study three important problems: dendrogram description, dendrogram combination, and dendrogram selection. We develop two approaches for dendrogram selection based on tree distances, and we investigate various dendrogram distances for representing dendrograms. We provide a systematic empirical study of the ensemble hierarchical clustering problem. Experimental results demonstrate the effectiveness of our proposed approaches.