Clusters Of Arbitrary Shapes Research Articles

An improved DBSCAN algorithm based on cell-like P systems with promoters and inhibitors.

Density-based spatial clustering of applications with noise (DBSCAN) algorithm can find clusters of arbitrary shape, while the noise points can be removed. Membrane computing is a novel research branch of bio-inspired computing, which seeks to discover new computational models/framework from biological cells. The obtained parallel and distributed computing models are usually called P systems. In this work, DBSCAN algorithm is improved by using parallel evolution mechanism and hierarchical membrane structure in cell-like P systems with promoters and inhibitors, where promoters and inhibitors are utilized to regulate parallelism of objects evolution. Experiment results show that the proposed algorithm performs well in big cluster analysis. The time complexity is improved to O(n), in comparison with conventional DBSCAN of O(n2). The results give some hints to improve conventional algorithms by using the hierarchical framework and parallel evolution mechanism in membrane computing models.

StreamSW: A density-based approach for clustering data streams over sliding windows

Density-based clustering is a prominent and an essential technique in mining data streams. It can discover clusters of arbitrary or irregular shape and handle noisy data. This paper presents StreamSW, a new density-based approach for clustering streaming data over a sliding window (SW). A Sliding window is an extensively adopted window model for capturing and mining streaming data. The StreamSW approach adopts a two-phase framework for performing clustering on streaming data. In the online phase, the p-micro-clusters and grid structure are adopted to hold a synopsis of the streaming data. In the offline phase, final macro-clusters are created from the p-micro-clusters of online phase using the conventional DBSCAN algorithm. The StreamSW approach discovers the clusters with an irregular shape in limited memory and time. Experimental results exhibit that the speed and quality of StreamSW are better than the current approaches.

REDPC: A residual error-based density peak clustering algorithm

The density peak clustering (DPC) algorithm was designed to identify arbitrary-shaped clusters by finding density peaks in the underlying dataset. Due to its aptitudes of relatively low computational complexity and a small number of control parameters in use, DPC soon became widely adopted. However, because DPC takes the entire data space into consideration during the computation of local density, which is then used to generate a decision graph for the identification of cluster centroids, DPC may face difficulty in differentiating overlapping clusters and in dealing with low-density data points. In this paper, we propose a residual error-based density peak clustering algorithm named REDPC to better handle datasets comprising various data distribution patterns. Specifically, REDPC adopts the residual error computation to measure the local density within a neighbourhood region. As such, comparing to DPC, our REDPC algorithm provides a better decision graph for the identification of cluster centroids and better handles the low-density data points. Experimental results on both synthetic and real-world datasets show that REDPC performs better than DPC and other algorithms.

Relative Density Clustering Algorithm Based on Density Fluctuation

With strong ability of noise resistance and discovery clusters of arbitrary shapes makes, the traditional density-based clustering algorithm has been widely used in clustering analysis. However, the quality of clustering results would be reduced significantly when the traditional density clustering algorithm was used to analyze uneven density datasets. Though the classical OPTICS algorithm can identify the clusters with uneven density, it is useless to the clusters whose boundaries are adjacent or mixed. To overcome this problem, a density fluctuation-based relative density clustering algorithm, named DFRDC (Relative Density Clustering Algorithm Based on Density Fluctuation) is proposed. The experimental results show that DFRDC can effectively identify multiple clusters with different densities and outperform of the state-of-the-art density clustering algorithms.

A new clustering validity index for arbitrary shape of clusters

In clustering problems, the correct number of clusters is usually unknown. Thus, all clusters produced by clustering algorithms should be evaluated, and the correct number of clusters is then selected based on a cluster validity index (CVI). CVI has been popularly used to evaluate the fitness of partitions by clustering algorithms. CVI is measured by the summation or ratio of compactness and separation measures, in which compactness refers to the concentration of data in each cluster, and separation refers to the intra-cluster distances. However, the existing CVIs are sensitive to clusters with arbitrary shapes, especially for high-dimensional data. In addition, the values of existing validity indices can be heavily influenced by noise and outliers. Therefore, in this paper, we propose a support vector data description (SVDD)-based CVI, in which the compactness of a cluster is measured in the kernel space, in an attempt to overcome the sensitivity of a compactness measure for arbitrary shapes, sub-clusters, and noise in data. The proposed CVI is evaluated through a series of experiments and shows that the SVDD variants cannot successfully determine the correct cluster number for most cases, but they can for cases with heavy overlapping and outliers, especially for arbitrary and overlapping shapes, compared to non-SVDD approaches on most datasets.

A novel clustering algorithm based on PageRank and minimax similarity

Clustering by fast search and find of density peaks (herein called FDPC), as a recently proposed density-based clustering algorithm, has attracted the attention of many researchers since it can recognize arbitrary-shaped clusters. In addition, FDPC needs only one parameter $$d_c$$ and identifies the number of clusters by decision graph. Nevertheless, it is not clear how to find a proper $$d_c$$ for a given data set and such a perfect parameter may not exist in practice for the multi-scale data set. In this paper, we proposed a modified PageRank algorithm to compute the local density for each data point which is more robust than Gaussian kernel and cutoff method. Besides, FDPC yields poor results on the random distribution data sets since there may be several maxima for one cluster. To solve this problem, we proposed an improved minimax similarity method. Comparing our proposed approach with FDPC on some artificial and real-life data sets, the experimental results indicate that our proposed approach outperforms FDPC in terms of accuracy.

A hierarchical clustering algorithm based on noise removal

Noise is irrelevant or meaningless data and hinders most types of data analysis. The existing clustering algorithms seldom take the noise points into consideration and cannot detect arbitrary-shaped clusters. This paper presents a Hierarchical Clustering algorithm Based on Noise Removal (HCBNR). It is robust against noise points and good at discovering clusters with arbitrary shapes. In this work, natural neighbor-based density is applied to remove noise points in a data set firstly. Then we construct a saturated neighbor graph on the rest points, and a novel modularity-based graph partitioning algorithm is used to divide the graph into small clusters. Finally, the small clusters are repeatedly merged according to a novel similarity metric between clusters until the desired cluster number is obtained. The experimental results on synthetic data sets and real data sets show that our method can accurately identify noise points and obtain better clustering results than existing clustering algorithms when discovering arbitrary-shaped clusters.

Estimation of Algorithms Efficiency in the Task of Biological Objects Clustering

Background. The task of determining the functional relationship between biophysical parameters is an integral part of the actual problem of finding the optimal impact on a biological object and is currently not completely resolved. One of the important tasks in this area is the partitioning of the original feature space into such areas (clusters) that relate to different functional relationships linking biophysical parameters and have, in general, an arbitrary shape. Such clusters in the future is logical to call functional. To obtain and analyze the functional clusters, there are a number of algorithms, each of which has its advantages and disadvantages. At the same time, the solution of a certain practical problem requires an evaluation of the efficiency of the algorithms in terms of the cluster separation adequacy.Objective. In this paper, for a general example of the biological objects clustering problem (Fischer’s Iris Data Set), the efficiency of a typical clustering tools series is evaluated. The application of k-means classical algorithm, the Ward algorithm and developed in this work the fuzzy version of clustering for the k-means algorithm with a limited mass of the working area for the clusters’ formation was considered.Methods. The algorithm includes a procedure for a priori estimation of the clusters quantity. The estimation is carried out according to the frequency histogram. To determine the optimal number of the histogram columns, the application of the Scott formula is justified. The algorithm allows forming clusters of arbitrary configuration with obtaining the value of the object's membership measure for each of the clusters. The comparative testing of the above algorithms was carried out on Fisher’s Iris Data Set.Results. The best value of F1-score is obtained for the algorithm proposed in this paper: F1 = 0.92, the value F1 = 0.90 is obtained for the Ward method and the value F1 = 0.88 – for the classical k-means algorithm.Conclusions. The obtained test results on the analysis problem of arbitrary-shaped clusters made it possible to give preference to the version of fuzzy k-means with a limited mass of the working area for the clusters’ formation. The calculating of the membership measure value allows us to obtain additional information on the structure of cluster formations, as well as to correct the result of clustering of k-means with a limited mass, which is especially important since the formation of clusters occurs in a single pass. Comparing the computational resources required for computing algorithms with relatively close test results also makes it possible to give preference to the developed algorithm. Compared with the Ward algorithm, it requires fewer computing resources since no additional memory is needed to store the distance matrix and no time is required to recalculate it.

An Eigenspace approach for detecting multiple space-time disease clusters: Application to measles hotspots detection in Khyber-Pakhtunkhwa, Pakistan.

Identifying the abnormally high-risk regions in a spatiotemporal space that contains an unexpected disease count is helpful to conduct surveillance and implement control strategies. The EigenSpot algorithm has been recently proposed for detecting space-time disease clusters of arbitrary shapes with no restriction on the distribution and quality of the data, and has shown some promising advantages over the state-of-the-art methods. However, the main problem with the EigenSpot method is that it cannot be adapted to detect more than one spatiotemporal hotspot. This is an important limitation, since, in reality, we may have multiple hotspots, sometimes at the same level of importance. We propose an extension of the EigenSpot algorithm, called Multi-EigenSpot that is able to handle multiple hotspots by iteratively removing previously detected hotspots and re-running the algorithm until no more hotspots are found. In addition, a visualization tool (heatmap) has been linked to the proposed algorithm to visualize multiple clusters with different colors. We evaluated the proposed method using the monthly data on measles cases in Khyber-Pakhtunkhwa, Pakistan (Jan 2016- Dec 2016), and the efficiency was compared with the state-of-the-art methods: EigenSpot and Space-time scan statistic (SaTScan). The results showed the effectiveness of the proposed method for detecting multiple clusters in a spatiotemporal space.

An Efficient Density Based Clustering approach for High Dimensional Data

Data extraction, data processing, pattern mining and clustering are the important features in data mining. The extraction of data and formation of interesting patterns from huge datasets can be used in prediction and decision making for further analysis. This improves, the need for efficient and effective analysis methods to make use of this data. Clustering is one important technique in data mining. In clustering a set of items are divided into several clusters where inter-cluster similarity is minimized and intra-cluster similarity is maximized. Clustering techniques are easy to identify of class in large databases. However, the application to large databases rises the following requirements for clustering techniques: minimal requirements of domain knowledge to determine the input specifications, invention of clusters with absolute shape & certainty of large databases.. The existing clustering techniques offer no solution to the combination of requirements. The proposed clustering technique DBSCAN using KNN relying on a density-based notion of clusters which is accomplished to discover clusters of arbitrary shape.

High dimensional data clustering

Clustering becomes difficult due to the increasing sparsity of such data, as well as the increasing difficulty in distinguishing distances between data points. The proposed method called “kernel trick” and “Collective Neighbour Clustering”, which takes as input measures of correspondence between pairs of data points. Real-valued hubs are exchanged between data points until a high-quality set of patterns and corresponding clusters gradually emerges [2]. To validate our theory by demonstrating that hubness is a high-quality measure of point centrality within a high dimensional information cluster, and by proposing several hubness-based clustering algorithms, showing that main hubs can be used effectively as cluster prototypes or as guides during the search for centroid-based cluster patterns [4]. Experimental results demonstrate the good performance of our proposed algorithms in manifold settings, mainly focused on large quantities of overlapping noise. The proposed methods are modified mostly for detecting approximately hyper spherical clusters and need to be extended to properly handle clusters of arbitrary shapes [6]. For this purpose, we provide an overview of approaches that use quality metrics in high-dimensional data visualization and propose systematization based on a thorough literature review. We carefully analyze the papers and derive a set of factors for discriminating the quality metrics, visualization techniques, and the process itself [10]. The process is described through a reworked version of the well-known information visualization pipeline. We demonstrate the usefulness of our model by applying it to several existing approaches that use quality metrics, and we provide reflections on implications of our model for future research. High-dimensional data arise naturally in many domains, and have regularly presented a great challenge for traditional data-mining techniques, both in terms of effectiveness and efficiency [7]. Clustering becomes difficult due to the increasing sparsity of such data, as well as the increasing difficulty in distinguishing distances between data points. In this paper we take a novel perspective on the problem of clustering high-dimensional data [8]. Instead of attempting to avoid the curse of dimensionality by observing a lower-dimensional feature subspace, we embrace dimensionality by taking advantage of some inherently high-dimensional phenomena. More specifically, we show that hubness, i.e., the tendency of high-dimensional data to contain points (hubs) that frequently occur in k-nearest neighbour lists of other points, can be successfully exploited in clustering. We validate our hypothesis by proposing several hubness-based clustering algorithms and testing them on high-dimensional data. Experimental results demonstrate good performance of our algorithms in multiple settings, particularly in the presence of large quantities of noise [9].

Adaptive clustering algorithm based on kNN and density

Although many clustering algorithms have been proposed, they all have various limitations. Existing clustering algorithms usually require the user to set the appropriate threshold parameters and those parameters are usually not adaptive. In this paper, a new clustering method is proposed. Firstly, the k nearest neighbors of all samples is calculated, and then a density method based on kNN is used to complete the clustering process. In order to achieve this goal, a statistics alpha is proposed for measuring the degree of denseness or sparseness of distribution of the entire samples, and a statistical model is proposed to calculate the local parameters, beta and gamma. That is, the category of each sample is determined by the combination of kNN with density. That is to say, the total number of samples determines an appropriate k value to obtain the ordered kNN of every sample, and then the radius of surrounding region (SR) is calculated by 5NN of all samples. Furthermore, the density of every sample is calculated. In the whole process of clustering, the global threshold is determined by the density distribution of all samples, and then the local threshold is self-adaptive. All sample density is sorted to search automatically for clusters from the highest point of density of the distribution of all samples. The algorithm can not only discover clusters of arbitrary shapes and automatically remove noise and outliers, but also it can find clusters with different densities and those with internal density variation. The results of experiments on the synthetic data and human face image data demonstrate that the algorithm is effective. The code is available under the following URL: https://github.com/bing-shi/Acnd.

A Parallel Community Detection Algorithm for Big Social Networks

Mining social networks has become an important task in data mining field, which describes users and their roles and relationships in social networks. Processing social networks with graph algorithms is the source for discovering many features. The most important algorithms applied to social networks are community detection algorithms. Communities of social networks are groups of people sharing common interests or activities. DenGraph is one of the density-based algorithms that used to find clusters of arbitrary shapes based on users’ interactions in social networks. However, because of the rapidly growing size of social networks, it is impossible to process a huge graph on a single machine in an acceptable level of execution. In this article, DenGraph algorithm has been redesigned to work in distributed computing environment. We proposed ParaDengraph Algorithm based on Pregel parallel model for large graph processing.

A new kernel-based possibilistic intuitionistic fuzzy c-means clustering

Fuzzy c-means and its derivatives such as possibilistic c-means and possibilistic fuzzy c-means are the most widely used clustering algorithms in the literature. Though efficient, these clustering algorithms do not achieve high cluster quality on real-world datasets, which are not linearly separable. Kernel-based clustering algorithms employ nonlinear similarity measures to define the inter-point similarities. As a result, they are able to identify clusters of arbitrary shapes and densities. Comparative analysis over standard datasets has established the superiority of kernel methods over its corresponding standard algorithms. In this paper, we propose a kernel-based Atanassov's possibilistic intuitionistic fuzzy clustering for data clustering and image segmentation. The paper explores the performance of the proposed methodology with respect to various internal and external indices for various real datasets and it is found to perform better than other clustering techniques in the sequel, i.e., normal as well as kernel-based algorithms. Experimental results on noisy image datasets also show the competence of the proposed approach.

Density core-based clustering algorithm with dynamic scanning radius

Clustering analysis has been widely used in many fields such as image segmentation, pattern recognition, data analysis, market researches and so on. However, the distribution patterns of clusters are natural and complex in many research areas. In other words, most real data sets are non-spherical or non-elliptical clusters. For example, face images and hand-writing digital images are distributed in manifolds and some biological data sets are distributed in hyper-rectangles. Therefore, it is a great challenge to detect clusters of arbitrary shapes in multi-density datasets. Most of previous clustering algorithms cannot be applied to complex patterns with large variations in density because they only find hyper-elliptical and hyper-spherical clusters through centroid-based clustering approaches or fixed global parameters. This paper presents DCNaN, a clustering algorithm based on the density core and the natural neighbor to recognize complex patterns with large variations in density. Density cores can roughly retain the shape of clusters and natural neighbors are introduced to find dynamic scanning radiuses rather than fixed global parameters. The results of our experiments show that compared to state-of-the-art clustering techniques, our algorithm achieves better clustering quality, accuracy and efficiency, especially in recognizing extremely complex patterns with large variations in density.

Density Based Cluster Growing via Dominant Sets

Although there are a lot of clustering algorithms available in the literature, existing algorithms are usually afflicted by practical problems of one form or another, including parameter dependence and the inability to generate clusters of arbitrary shapes. In this paper we aim to solve these two problems by merging the merits of dominant sets and density based clustering algorithms. We firstly apply histogram equalization to eliminate the parameter dependence problem of the dominant sets algorithm. Noticing that the obtained clusters are usually smaller than the real ones, a density threshold based cluster growing step is then used to improve the clustering results, where the involved parameters are determined based on the initial clusters. This is followed by the second cluster growing step which makes use of the density relationship between neighboring data. Data clustering experiments and comparison with other algorithms validate the effectiveness of the proposed algorithm.

Effective community division based on improved spectral clustering

Abstract Not only does attribute of nodes affect the effectiveness and efficiency of community division, but also the relationship of them has a great impact on it. Clusters of arbitrary shape can be identified by the Spectral Clustering (SC). However, k-means clustering used in SC still could result in local optima, and the parameters in Radial Basis Function need to be determined by trial and error. In order to make such algorithm better fit into community division of social network, we try to merge attribute and relationship of node and optimize the ability of spectral clustering to get the global solution, thus a new community clustering algorithm called Spectral Clustering Based on Simulated Annealing and Particle swarm optimization (SCBSP) is proposed. The proposed algorithm is adapted to social networking division. In related experiments, the proposed algorithm, which enhances the global searching ability, has better global convergence and makes better performance in community division than original spectral clustering.

Effective Mapping of Urban Areas Using ENVISAT ASAR, Sentinel-1A, and HJ-1-C Data

This letter presents a methodology for urban area mapping with density-based spatial clustering of applications with noise (DBSCAN) using the Advanced Synthetic Aperture Radar (ASAR), Sentinel-1A, and HuanJing-1C data. Urban areas have a diversity of shapes, including circles, squares, strips, and other irregular shapes, and the DBSCAN clustering algorithm is suitable for identifying clusters of arbitrary shapes. Exploiting DBSCAN to extract urban areas is a key aspect of this method, and improvements via the incorporation of synthetic aperture radar data preprocessing and postprocessing also play important roles in optimizing the extractions. Different test site sizes were chosen to demonstrate the effectiveness and feasibility of the proposed method, and the validation results showed that the method is efficient and accurately extracts urban areas ranging from small towns to super metropolitan areas.

FRSVC: Towards making support vector clustering consume less

In spite of with great advantage of discovering arbitrary shapes of clusters, support vector clustering (SVC) is frustrated by large-scale data, especially on resource limited platform. It is due to pricey storage and computation consumptions from solving dual problem and labeling clusters upon the pre-computed kernel matrix and sampling point pairs, respectively. Towards on it, we first present a dual coordinate descent method to reformulate the solver that leads to a flexible training phase carried out on any runtime platform with/without sufficient memory. Then, a novel labeling phase who does connectivity analysis between two nearest neighboring decomposed convex hulls referring to clusters is proposed, in which a new designed strategy namely sample once connected checking first tries to reduces the scope of sampling analysis. By integrating them together, a faster and reformulated SVC (FRSVC) is created with less consumption achieved according to comparative analysis of time and space complexities. Furthermore, experimental results confirm a significant improvement on flexibility of selective efficiency without losing accuracy, with which a balance can be easily reached on the basis of resources a platform equipped.

Clustering by fast search and merge of local density peaks for gene expression microarray data

Clustering is an unsupervised approach to classify elements based on their similarity, and it is used to find the intrinsic patterns of data. There are enormous applications of clustering in bioinformatics, pattern recognition, and astronomy. This paper presents a clustering approach based on the idea that density wise single or multiple connected regions make a cluster, in which density maxima point represents the center of the corresponding density region. More precisely, our approach firstly finds the local density regions and subsequently merges the density connected regions to form the meaningful clusters. This idea empowers the clustering procedure, in which outliers are automatically detected, higher dense regions are intuitively determined and merged to form clusters of arbitrary shape, and clusters are identified regardless the dimensionality of space in which they are embedded. Extensive experiments are performed on several complex data sets to analyze and compare our approach with the state-of-the-art clustering methods. In addition, we benchmarked the algorithm on gene expression microarray data sets for cancer subtyping; to distinguish normal tissues from tumor; and to classify multiple tissue data sets.