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.
As an example, LDBSCAN (Local-Density Based Spatial Clustering for Applications with Noise) @cite_51 uses a slightly modified model that provides the definition of local density to identify non-isodensity clusters.
@cite_51
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Density-based clustering algorithms are attractive for the task of class identification in spatial database. However, in many cases, very different local-density clusters exist in different regions of data space, therefore, DBSCAN method [M. Ester, H.-P. Kriegel, J. Sander, X. Xu, A density-based algorithm for discovering clusters in large spatial databases with noise, in: E. Simoudis, J. Han, U.M. Fayyad (Eds.), Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, Portland, OR, AAAI, Menlo Park, CA, 1996, pp. 226-231] using a global density parameter is not suitable. Although OPTICS [M. Ankerst, M.M. Breunig, H.-P. Kriegel, J. Sander, OPTICS: ordering points to identify the clustering structure, in: A. Delis, C. Faloutsos, S. Ghandeharizadeh (Eds.), Proceedings of ACM SIGMOD International Conference on Management of Data Philadelphia, PA, ACM, New York, 1999, pp. 49-60] provides an augmented ordering of the database to represent its density-based clustering structure, it only generates the clusters with local-density exceeds certain thresholds but not the cluster of similar local-density; in addition, it does not produce clusters of a data set explicitly. Furthermore, the parameters required by almost all the major clustering algorithms are hard to determine although they significantly impact on the clustering result. In this paper, a new clustering algorithm LDBSCAN relying on a local-density-based notion of clusters is proposed. In this technique, the selection of appropriate parameters is not difficult; it also takes the advantage of the LOF [M.M. Breunig, H.-P. Kriegel, R.T. Ng, J. Sander, LOF: identifying density-based local outliers, in: W. Chen, J.F. Naughton, P.A. Bernstein (Eds.), Proceedings of ACM SIGMOD International Conference on Management of Data, Dalles, TX, ACM, New York, 2000, pp. 93-104] to detect the noises comparing with other density-based clustering algorithms. The proposed algorithm has potential applications in business intelligence. Subspace clustering mines clusters hidden in subspaces of high-dimensional data sets. Density-based approaches have been shown to successfully mine clusters of arbitrary shape even in the presence of noise in full space clustering. Exhaustive search of all density-based subspace clusters, however, results in infeasible runtimes for large high-dimensional data sets. This is due to the exponential number of possible subspace projections in addition to the high computational cost of density-based clustering. In this paper, we propose lossless efficient detection of density-based subspace clusters. In our EDSC (efficient density-based subspace clustering) algorithm we reduce the high computational cost of density-based subspace clustering by a complete multistep filter-and-refine algorithm. Our first hypercube filter step avoids exhaustive search of all regions in all subspaces by enclosing potentially density-based clusters in hypercubes. Our second filter step provides additional pruning based on a density monotonicity property. In the final refinement step, the exact unbiased density-based subspace clustering result is detected. As we prove that pruning is lossless in both filter steps, we guarantee completeness of the result. In thorough experiments on synthetic and real world data sets, we demonstrate substantial efficiency gains. Our lossless EDSC approach outperforms existing density-based subspace clustering algorithms by orders of magnitude. Clustering is one of the basic data mining tasks that can be used to extract hidden information from data in the absence of target classes. One of the most well-known density based clustering algorithms for processing spatial data is Density-Based Spatial Clustering of Application with Noise (DBSCAN) that uses learning parameters epsiv and minPts to define the density that will be sought in the data set while forming the clusters. The major drawbacks of the DBSCAN algorithm are its sensitivity to user input required to execute the algorithm, inability to recognize clusters with different densities, and computational complexity. In this study, we propose a three-level clustering method to address the second issue. The first level selects appropriate grids so that the density is homogeneous in each grid. The second stage merges cells with similar densities and identifies the most suitable values of epsiv and minPts in each grid that remain after merging. The third step of the proposed method executes the DBSCAN method with these identified parameters in the dataset. The proposed method is tested in three artificial benchmark data sets to demonstrate that the clusters are correctly identified. Subspace clustering is a problem of finding a multi-subspace representation that best fits sample points drawn from a high-dimensional space. The existing clustering models generally adopt different norms to describe noise, which is equivalent to assuming that the data are corrupted by specific types of noise. In practice, however, noise is much more complex. So it is inappropriate to simply use a certain norm to model noise. Therefore, we propose Mixture of Gaussian Regression (MoG Regression) for subspace clustering by modeling noise as a Mixture of Gaussians (MoG). The MoG Regression provides an effective way to model a much broader range of noise distributions. As a result, the obtained affinity matrix is better at characterizing the structure of data in real applications. Experimental results on multiple datasets demonstrate that MoG Regression significantly outperforms state-of-the-art subspace clustering methods.