A varied density-based clustering algorithm

Finding clusters of different densities is a challenging task. DBSCAN “Density-Based Spatial Clustering of Applications with Noise” method has trouble discovering clusters of various densities since it uses a fixed radius. This article proposes an extended DBSCAN for finding clusters of different densities. The proposed method uses a dynamic radius and assigns a regional density value for each object, then counts the objects of similar density within the radius. If the neighborhood size ≥ MinPts, then the object is a core, and a cluster can grow from it, otherwise, the object is assigned noise temporarily. Two objects are similar in local density if their similarity ≥ threshold. The proposed method can discover clusters of any density from the data effectively. The method requires three parameters; MinPts, Eps (distance to the kth neighbor), and similarity threshold. The practical results show the superior ability of the suggested method to detect clusters of different densities even with no discernible separations between them.

Enhancing density-based clustering: Parameter reduction and outlier detection

Stream data applications have become more and more prominent recently and the requirements for stream clustering algorithms have increased drastically. Due to continuously evolving nature of the stream, it is crucial that the algorithm autonomously detects clusters of arbitrary shape, with different densities, and varying number of clusters. Although available density-based stream clustering are able to detect clusters with arbitrary shapes and varying numbers, they fail to adapt their thresholds to detect clusters with different densities. In this paper we propose a stream clustering algorithm called HASTREAM, which is based on a hierarchical density-based clustering model that automatically detects clusters of different densities. The density thresholds are independently adapted to the existing data without the need of any user intervention. To reduce the high computational cost of the presented approach, techniques from the graph theory domain are utilized to devise an incremental update of the underlying model. To show the effectiveness of HASTREAM and hierarchical density-based approaches in general, several synthetic and real world data sets are evaluated using various quality measures. The results showed that the hierarchical property of the model was able to improve the quality of density-based stream clusterings and enabled HASTREAM to detect streaming clusters of different densities.

DBSCAN is a well-known density based clustering algorithm, which can discover clusters of different shapes and sizes along with outliers. However, it suffers from major drawbacks like high computational cost, inability to find varied density clusters and dependency on user provided input density parameters. To address these issues, we propose a novel density based clustering algorithm titled, VDMR-DBSCAN (Varied Density MapReduce DBSCAN), a scalable DBSCAN algorithm using MapReduce which can detect varied density clusters with automatic computation of input density parameters. VDMR-DBSCAN divides the data into small partitions which are parallely processed on Hadoop platform. Thereafter, density variations in a partition are analyzed statistically to divide the data into groups of similar density called Density level sets (DLS). Input density parameters are estimated for each DLS, later DBSCAN is applied on each DLS using its corresponding density parameters. Most importantly, we propose a novel merging technique, which merges the similar density clusters present in different partitions and produces meaningful and compact clusters of varied density. We experimented on large and small synthetic datasets which well confirms the efficacy of our algorithm in terms of scalability and ability to find varied density clusters.

In clustering spatial data, we are given a set of points in Rn and the objective is to find the clusters (representing spatial objects) in the set of points. Finding clusters with different shapes, sizes, and densities in data with noise and potentially outliers is a challenging task. This problem is especially studied in machine learning community and has lots of applications. We present a novel clustering technique, which can solve mentioned issues considerably. In the proposed algorithm, we let the structure of the data set itself find the clusters, this is done by having points actively send and receive feedbacks to each other.The idea of the proposed method is to transform the input data set into a graph by adding edges between points that belong to the same cluster, so as connected components correspond to clusters, whereas points in different clusters are almost disconnected. At the start, our algorithm creates a preliminary graph and tries to improve it iteratively. In order to build the graph (add more edges), each point sends feedback to its neighborhood points. The neighborhoods and the feedback to be sent are determined by investigating the received feedbacks. This process continues until a stable graph is created. Henceforth, the clusters are formed by post-processing the constructed graph. Our algorithm is intuitive, easy to state and analyze, and does not need to have lots of parameter tuning. Experimental results show that our proposed algorithm outperforms existing related methods in this area.

An efficient and scalable density-based clustering algorithm for datasets with complex structures

Several clustering algorithms have been extensively used to analyze vast amounts of spatial data. One of these algorithms is the SNN (Shared Nearest Neighbor), a density-based algorithm, which has several advantages when analyzing this type of data due to its ability of identifying clusters of different shapes, sizes and densities, as well as the capability to deal with noise. Having into account that data are usually progressively collected as time passes, incremental clustering approaches are required when there is the need to update the clustering results as new data become available. This paper proposes SNN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">++</sup> , an incremental clustering algorithm based on the SNN. Its performance and the quality of the resulting clusters are compared with the SNN and the results show that the SNN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">++</sup> yields the same result as the SNN and show that the incremental feature was added to the SNN without any computational penalty. Moreover, the experimental results also show that processing huge amounts of data using increments considerably decreases the number of distances that need to be computed to identify the points' nearest neighbors.

Wide spread clustering algorithms use the Euclidean distance to measure spatial proximity. However, obstacles in other GIS data-layers prevent traversing the straight path between two points. AUTOCLUST+ clusters points in the presence of obstacles based on Voronoi modeling and Delaunay Diagrams. The algorithm is free of usersupplied arguments and incorporates global and local variations. Thus, it detects high-quality clusters (clusters of arbitrary shapes, clusters of different densities, sparse clusters adjacent to high-density clusters, multiple bridges between clusters and closely located high-density clusters) without prior knowledge. Consequently, it successfully supports correlation analyses between layers (requiring high-quality clusters) and more general locational optimization problems in the presence of obstacles. All this within O(n log n+[m+R] log n) expected time, where n is the number of data points, m is the number of line-segments that determine the obstacles and R is the number of Delaunay edges intersecting some obstacles. A series of detailed performance evaluations illustrates the power of AUTOCLUST+ and confirms the virtues of our approach.

The clustering of spatio‐temporal events has become one of the most important research branches of spatio‐temporal data mining. However, the discovery of clusters of spatio‐temporal events with different shapes and densities remains a challenging problem because of the subjectivity in the choice of two critical parameters: the spatio‐temporal window for estimating the density around each event, and the density threshold for evaluating the significance of clusters. To make the clustering of spatio‐temporal events objective, in this study these two parameters were adaptively generated from statistical information about the dataset. More precisely, the density threshold was statistically modeled as an adjusted significance level controlled by the cardinality and support domain of the dataset, and the appropriate sizes of spatio‐temporal windows for clustering were determined by the spatio‐temporal classification entropy and stability analysis. Experiments on both simulated and earthquake datasets were conducted, and the results show that the proposed method can identify clusters of different shapes and densities.

Spatial-temporal clustering is very useful unsupervised learning technique and can be used to identify interesting distribution patterns from geo-located data. It is one of the most commonly used data mining techniques in many application domains, e.g. geographic information science, health science, and environmental science. In this paper, we propose a density-based spatial-temporal clustering algorithm for geo-located data points, based on an extension of the SNN (Shared Nearest Neighbor) clustering. The proposed algorithm allows the integration of location, time and other semantic attributes in the clustering process. This algorithm can find clusters of different sizes, shapes, and densities in noisy data. We evaluate the effectiveness of our algorithm through a case study involving a New York City taxi cab pickup data and Maryland crime data. The experimental results show that the proposed algorithm can discover interesting patterns and useful information from spatial-temporal data.

Statistical and density-based clustering of geographical flows for crowd movement patterns recognition

A grid-density based technique for finding clusters in satellite image

FACADE (Fast and Automatic Clustering Approach to Data Engineering) is a spatial clustering tool that can discover clusters of different sizes, shapes, and densities in noisy spatial data. Compared with the existing clustering methods, FACADE has several advantages: first, it separates true data and noise more effectively. Second, most steps of FACADE are automatic. Third, it requires only O(nlogn) time. 2D and 3D visualizations are used in FACADE to assist parameter selection and result evaluation. More information on FACADE is available at: http://viscomp.utdallas.edu/FACADE.

Fuzzy c-means clustering is a useful method for capturing group-level heterogeneity of objects. This method estimates cluster centroids and fuzzy memberships simultaneously. A potential limitation of fuzzy c-means is that it may fail to detect clusters of different sizes. To address this difficulty, we propose an extension of FCM, called hierarchically structured FCM, which can detect clusters of different sizes as well as provide additional information on nested structures of clusters. Unlike extant hierarchical extensions of FCM that execute FCM at each level of hierarchy separately in a sequential manner, the proposed method estimates cluster centroids and fuzzy memberships in different levels simultaneously by minimizing a single objective function. The optimal number of clusters and sub-clusters is determined by examining cluster validity measures. The usefulness of the proposed method is illustrated by analyzing two synthetic data and real image data.

The density-based clustering method is considered a robust approach in unsupervised clustering technique due to its ability to identify outliers, form clusters of irregular shapes and automatically determine the number of clusters. These unique properties helped its pioneering algorithm, the Density-based Spatial Clustering on Applications with Noise (DBSCAN), become applicable in datasets where various number of clusters of different shapes and sizes could be detected without much interference from the user. However, the original algorithm exhibits limitations, especially towards its sensitivity on its user input parameters minPts and ɛ. Additionally, the algorithm assigned inconsistent cluster labels to data objects found in overlapping density regions of separate clusters, hence lowering its accuracy. To alleviate these specific problems and increase the clustering accuracy, we propose two methods that use the statistical data from a given dataset's k-nearest neighbor density distribution in order to determine the optimal ɛ values. Our approach removes the burden on the users, and automatically detects the clusters of a given dataset. Furthermore, a method to identify the accurate border objects of separate clusters is proposed and implemented to solve the unpredictability of the original algorithm. Finally, in our experiments, we show that our efficient re-implementation of the original algorithm to automatically cluster datasets and improve the clustering quality of adjoining cluster members provides increase in clustering accuracy and faster running times when compared to earlier approaches.