Representative Clustering Research Articles

Hyperplane Division in Fuzzy C-Means: Clustering Big Data

Big data with a large number of observations (samples) have posed genuine challenges for fuzzy clustering algorithms and fuzzy C-means (FCM), in particular. In this article, we propose an original algorithm referred to as a hyperplane division method to split the entire data set into disjoint subsets. By disjoint subsets, we mean that the data subspaces (parts of the entire data space), each of which is supported or spanned by the data points in the corresponding subset, do not overlap each other. The disjoint subsets turned out to be beneficial to the improvement of the quality of the clusters formed by the clustering algorithms. Moreover, considering that either a large number (say, thousands) or a small number (say, a few) of clusters may be pursued in the clustering task, we propose corresponding strategies (based on the hyperplane division method) to make clustering processes feasible, efficient, and effective. By validating the proposed strategies on both synthetic and publicly available data, we show their superiority (in terms of both efficiency and effectiveness) manifested in a visible way over the method of clustering the entire data and over some representative big data clustering methods.

Ordered smooth representation clustering

The smooth representation (SMR) model is a widely used segmentation method in computer vision. This model adopts the K nearest neighbour (KNN) graph to select samples for representation. All neighbours in the KNN graph are assumed to be equally important candidates. In this paper, we use special weights that are calculated by a novel cross-view kernel function to evaluate the contributions of neighbours to the subspace clustering in SMR. The neighbours that are found by the Gaussian similarity formula can be considered long-range similar neighbours. We add another item to accurately reflect the order relation in the cross-view kernel function. This addition allows the kernel function to generalize the conventional SMR method for sequential data. The ordered smooth representation (OSMR) model outperforms other representative space clustering methods on public datasets, namely, the UCI database, the USPS database, Yale B datasets, the Freiburg–Berkeley Motion Segmentation database and a real-world mobile video that was captured by a smart phone.

A novel hierarchical clustering approach based on data gravitation model

The purpose of clustering is to group the data points into several clusters according to their similarity. Inspired by law of gravitation, each data point considered as an object is exposed in data space and influenced by the data gravitation of the other data points. In this paper, a novel hierarchical clustering approach (NGHC) is proposed based on local data gravitation. Firstly, the dataset is partitioned into some clusters as intermediate result by a simple gravity-based clustering approach. Then the intermediate clusters are merged by a new linkage measure which combines the data gravitations between two clusters until the satisfactory result is obtained. Two real-world datasets are used to validate the clustering performance of NGHC compared with five representative clustering algorithms. The results exhibit that the NGHC algorithm obtains the best performance on low- and high-dimensional datasets.

Transfer learning-assisted multi-objective evolutionary clustering framework with decomposition for high-dimensional data

Although multi-objective evolutionary subspace clustering approaches have shown promise in handling high-dimensional datasets, their performance is restricted by two main drawbacks. First, their local search strategies have not been well investigated. Second, while exploring the search space, they neglect the useful knowledge from previously solved problems. To tackle these issues, this paper proposes a transfer learning-assisted multi-objective evolutionary clustering framework with decomposition. Firstly, we provide a decomposition-based local search strategy. To capture a comprehensive data structure, this strategy updates the weights of features by considering both the within-class compactness and between-class separation, and spontaneously balances the two properties. Secondly, we develop a knowledge transfer strategy. By transferring search experience from a previously solved clustering problem, the strategy improves the search efficiency, consequently enhances the clustering accuracy of the current problem. It has a closed-form solution and can transfer knowledge across both homogeneous and heterogeneous problems from either different or the same domains. Finally, we conduct an extensive experimental study on the framework by comparing with six representative subspace clustering approaches on a wide range of benchmarks and real-world applications. Results demonstrate the superiority of our framework.

Spatiotemporal Data Clustering: A Survey of Methods

Large quantities of spatiotemporal (ST) data can be easily collected from various domains such as transportation, social media analysis, crime analysis, and human mobility analysis. The development of ST data analysis methods can uncover potentially interesting and useful information. Due to the complexity of ST data and the diversity of objectives, a number of ST analysis methods exist, including but not limited to clustering, prediction, and change detection. As one of the most important methods, clustering has been widely used in many applications. It is a process of grouping data with similar spatial attributes, temporal attributes, or both, from which many significant events and regular phenomena can be discovered. In this paper, some representative ST clustering methods are reviewed, most of which are extended from spatial clustering. These methods are broadly divided into hypothesis testing-based methods and partitional clustering methods that have been applied differently in previous research. Research trends and the challenges of ST clustering are also discussed.

An ordered sparse subspace clustering algorithm based on p‐Norm

AbstractImages in video may include both Gaussian noise and geometric rotation. Thus, it is challenging to represent an image sequence in its intrinsically low‐dimensional space in a noise‐robust and rotation‐robust manner. In this paper, we propose a novel‐ordered sparse subspace clustering algorithm based on a p‐norm to achieve an effective clustering of sequential data under heavy noise conditions. We also use the wavelet‐histogram of oriented gradient (HOG) transform in the kernel view to extract both the global features (with the wavelet process) and the local features (with the HOG process) from the image. In addition, we assign different weights to different features to obtain a sparse coefficient matrix that helps to emphasize the global and local correlations in each sample. Similarly, the clustering algorithm based on the p‐norm for sequential images emphasizes the within‐class correlations amongst samples. Therefore, in this paper, we select additional denoising main components under a Laplacian constraint to achieve a better block‐diagonal structure and highlight the independence of different clusters. Extensive experiments performed on various public datasets (including the ordered face dataset, handwritten recognition dataset, video scene segmentation dataset, and object recognition dataset) demonstrate that the proposed method is more resilient to noise and rotation than other representative sparse subspace clustering methods.

Robust Semi-Supervised Non-Negative Matrix Factorization With Structured Normalization

Non-negative matrix factorization (NMF) approximates a non-negative data matrix with the product of two low-rank non-negative matrices by minimizing the cost of such approximation. However, traditional NMF models cannot be generalized in the cases when the dataset contains outliers and limited knowledge from domain experts. In this paper, we propose a robust semi-supervised NMF model (RSS-NMF) to overcome the aforementioned deficiency. RSS-NMF utilizes the L 2 /L 1 -norm to encourage approximation and makes the model insensitive to outliers by prohibiting them from dominating the cost function. To incorporate the discriminative information, RSS-NMF utilizes the structured normalization method when learns a diagonal matrix to normalize the coefficients such that they get close to the label indicators of the given labeled examples. Although the multiplicative update rule (MUR) can be adopted to minimize RSS-NMF, it converges slowly. In this paper, we adopt a fast gradient descent algorithm (FGD) to optimize RSS-NMF and prove its convergence to a stationary point. FGD uses a Newton method to search the optimal step length and thus, FGD converges faster than MUR. The experimental results show the promise of RSS-NMF comparing with the representative clustering models on several face image datasets.

Robust Subspace Clustering by Cauchy Loss Function.

Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-of-the-art approaches are designed by following the model of spectral clustering-based method. These methods pay much attention to learn the representation matrix to construct a suitable similarity matrix and overlook the influence of the noise term on subspace clustering. However, the real data are always contaminated by the noise and the noise usually has a complicated statistical distribution. To alleviate this problem, in this paper, we propose a subspace clustering method based on Cauchy loss function (CLF). Particularly, it uses CLF to penalize the noise term for suppressing the large noise mixed in the real data. This is due to that the CLF's influence function has an upper bound that can alleviate the influence of a single sample, especially the sample with a large noise, on estimating the residuals. Furthermore, we theoretically prove the grouping effect of our proposed method, which means that highly correlated data can be grouped together. Finally, experimental results on five real data sets reveal that our proposed method outperforms several representative clustering methods.

MMMs-Induced Possibilistic Fuzzy Co-Clustering and its Characteristics

In the field of cluster analysis, fuzzy theory including the concept of fuzzy sets has been actively utilized to realize flexible and robust clustering methods. FuzzyC-means (FCM), which is the most representative fuzzy clustering method, has been extended to achieve more robust clustering. For example, noise FCM (NFCM) performs noise rejection by introducing a noise cluster that absorbs noise objects and possibilisticC-means (PCM) performs the independent extraction of possibilistic clusters by introducing cluster-wise noise clusters. Similarly, in the field of co-clustering, fuzzy co-clustering induced by multinomial mixture models (FCCMM) was proposed and extended to noise FCCMM (NFCCMM) in an analogous fashion to the NFCM. Ubukata et al. have proposed noise clustering-based possibilistic co-clustering induced by multinomial mixture models (NPCCMM) in an analogous fashion to the PCM. In this study, we develop an NPCCMM scheme considering variable cluster volumes and the fuzziness degree of item memberships to investigate the specific aspects of fuzzy nature rather than probabilistic nature in co-clustering tasks. We investigated the characteristics of the proposed NPCCMM by applying it to an artificial data set and conducted document clustering experiments using real-life data sets. As a result, we found that the proposed method can derive more flexible possibilistic partitions than the probabilistic model by adjusting the fuzziness degrees of object and item memberships. The document clustering experiments also indicated the effectiveness of tuning the fuzziness degree of object and item memberships, and the optimization of cluster volumes to improve classification performance.

DISC: Disambiguating homonyms using graph structural clustering

Author name ambiguity degrades information retrieval, database integration, search results and, more importantly, correct attributions in bibliographic databases. Some unresolved issues include how to ascertain the actual number of authors, how to improve the performance and how to make the method more effective in terms of representative clustering metrics (average cluster purity, average author purity, K-metric, pairwise precision, pairwise recall, pairwise-F1, cluster precision, cluster recall and cluster-F1). It is a non-trivial task to disambiguate authors using only the implicit bibliographic information. An effective method ‘DISC’ is proposed that uses graph community detection algorithm, feature vectors and graph operations to disambiguate homonyms. The citation data set is pre-processed and ambiguous author blocks are formed. A co-authors graph is constructed using authors and their co-author’s relationships. A graph structural clustering ‘gSkeletonClu’ is applied to identify hubs, outliers and clusters of nodes in a co-author’s graph. Homonyms are resolved by splitting these clusters of nodes across the hub if their feature vector similarity is less than a predefined threshold. DISC utilises only co-authors and titles that are available in almost all bibliographic databases. With little modifications, DISC can also be used for entity disambiguation. To validate the DISC performance, experiments are performed on two Arnetminer data sets and compared with five previous unsupervised methods. Despite using limited bibliographic metadata, DISC achieves on average K-metric, pairwise-F1, and cluster-F1 of 92%, 84% and 74%, respectively, using Arnetminer-S and 86%, 80% and 57%, respectively, using Arnetminer-L. About 77.5% and 73.2% clusters are within the range (ground truth clusters ± 3) in Arnetminer-S and Arnetminer-L, respectively.

Updating the 97% identity threshold for 16S ribosomal RNA OTUs

The 16S ribosomal RNA (rRNA) gene is widely used to survey microbial communities. Sequences are often clustered into Operational Taxonomic Units (OTUs) as proxies for species. The canonical clustering threshold is 97% identity, which was proposed in 1994 when few 16S rRNA sequences were available, motivating a reassessment on current data. Using a large set of high-quality 16S rRNA sequences from finished genomes, I assessed the correspondence of OTUs to species for five representative clustering algorithms using four accuracy metrics. All algorithms had comparable accuracy when tuned to a given metric. Optimal identity thresholds were ∼99% for full-length sequences and ∼100% for the V4 hypervariable region. Reference sequences and source code are provided in the Supplementary Material. Supplementary data are available at Bioinformatics online.

K-DBSCAN: an efficient density-based clustering algorithm supports parallel computing

DBSCAN is the most representative density-based clustering algorithm and has been widely used in many fields. However, the running time of DBSCAN is unacceptable in many actual applications. To improve its performance, this paper presents a new 2D density-based clustering algorithm, K-DBSCAN, which successfully reduces the computational complexity of the clustering process by a simplified k-mean partitioning process and a reachable partition index, and enables parallel computing by a divide-and-conquer method. The experiments show that K-DBSCAN achieves remarkable accuracy, efficiency and applicability compared with conventional DBSCAN algorithms especially in large-scale spatial density-based clustering. The time complexity of K-DBSCAN is O(N2/KC), where K is the number of data partitions, and C is the number of physical computing cores.

K-DBSCAN: an efficient density-based clustering algorithm supports parallel computing

DBSCAN is the most representative density-based clustering algorithm and has been widely used in many fields. However, the running time of DBSCAN is unacceptable in many actual applications. To improve its performance, this paper presents a new 2D density-based clustering algorithm, K-DBSCAN, which successfully reduces the computational complexity of the clustering process by a simplified k-mean partitioning process and a reachable partition index, and enables parallel computing by a divide-and-conquer method. The experiments show that K-DBSCAN achieves remarkable accuracy, efficiency and applicability compared with conventional DBSCAN algorithms especially in large-scale spatial density-based clustering. The time complexity of K-DBSCAN is O(N2/KC), where K is the number of data partitions, and C is the number of physical computing cores.

A method for creating balanced cluster areas in wireless sensor networks

The balancing node energy is an important issue in sensor networks, since sensor nodes are deployed with a limited power in arbitrary regions. Clustering is one of the basic approaches for designing energy-efficient distributed sensor networks. In a representative clustering method, LEACH, cluster headers are elected based on a probability method. Therefore, cluster headers may be located by geographical randomness. Based on LEACH, there are some nodes which may do not belong within the transmission range of any cluster header or there are some nodes that are very far from their cluster header. The nodes that are far from their cluster header consume node energy quickly and it result in bad effects on working in sensor networks. The bad coverage of sensor networks gives a fatal effect on the QoS of the sensor application. In order to solve this problem, we propose a balanced clustering method that provides cluster headers to be geographically distributed evenly in entire clustered sensor networks. The experimental results show an excellent performance on the coverage of sensor networks and the life duration for the entire nodes of sensor networks.

WPO-EECRP: Energy-Efficient Clustering Routing Protocol Based on Weighting and Parameter Optimization in WSN

Clustering is an important way to realize energy saving in wireless sensor network. Combining the revelation of previous clustering protocols, we propose a new energy-efficient clustering routing protocol--WPO-EECRP. In order to achieve the goal of energy conservation, this protocol considers multiple clustering factors related to energy consumption to select cluster head such as residual energy, distance from node to base station, neighbors and number of neighbors through weighting, and finally transforms the question of efficient Clustering into the optimization of two parameters: neighbor communication range R and weight coefficient W of clustering factors. So the network is divided into clusters under the configuration of optimal parameters $$R_{opt}$$Ropt and $$W_{opt}$$Wopt, and operates until it completes data communication. Simulation results show that our proposed protocol can extend the network lifetime over 1.4 times as long as EECF and EACHP, two very representative clustering protocols published recently, significantly reduces the energy consumption, which has a good performance.

Combined constraint-based with metric-based in semi-supervised clustering ensemble

Recently, both semi-supervised clustering and cluster ensemble have received tremendous attention due to their accurate and reliable performance. There are mainly two kinds of existing semi-supervised clustering algorithms called constraint-based and metric-based. In this paper, we present a semi-supervised clustering ensemble approach which takes both pairwise constraints and metric measure into account. Firstly, under the assistance of supervised information included pairwise constraints and labeled data, the approach generates different base clustering partitions respectively using constraint-based semi-supervised clustering and metric-based semi-supervised clustering, in which the latter develops a new metric function. Given the spatial particularity of image pixels, the metric considers spatial distribution of surrounding pixels besides inherent features of pixels in the process of image feature extraction. And then the target clustering is obtained by integrating those base clustering partitions into an ensemble function. Finally, we conduct experimental verification on general data sets and image data sets, and compare clustering performance of our approach with those of other approaches. Both theoretical analysis and experimental results demonstrate that the proposed method produces considerable improvement in clustering accuracy and yields superior clustering results over a number of representative clustering methods.

Hierarchical seismic vulnerability assessment of power transmission systems: sensitivity analysis of fragility curves and clustering algorithms

This paper presents a sensitivity analysis of the hierarchical decomposition of networks in the context of seismic vulnerability of power systems. The sensitivity analysis is evaluated by varying the fragility curves and clustering algorithms on the vulnerability measure. For the fragility curves, four different curves are used. For sensitivity to clustering, four representative spectral clustering algorithms are used: SM, KVV, NJW, and Meila-Shi algorithms. The resulting vulnerability rankings are compared for a common case study (IEEE-118 test case) in terms of: correlation, identification of critical nodes, and identification of common clusters. The results show the robustness of the methodology with respect to variation of the fragility curves. On the other hand, the selection of the clustering algorithm is found to be a decisive parameter depending on application. If the application requires identification of critical elements a better performance is found.

On Fuzzy Non-Metric Model for Data with Tolerance and its Application to Incomplete Data Clustering

The fuzzy non-metric model (FNM) is a representative non-hierarchical clustering method, which is very useful because the belongingness or the membership degree of each datum to each cluster can be calculated directly from the dissimilarities between data and the cluster centers are not used. However, the original FNM cannot handle data with uncertainty. In this study, we refer to the data with uncertainty as “uncertain data,” e.g., incomplete data or data that have errors. Previously, a methods was proposed based on the concept of a tolerance vector for handling uncertain data and some clustering methods were constructed according to this concept, e.g. fuzzyc-means for data with tolerance. These methods can handle uncertain data in the framework of optimization. Thus, in the present study, we apply the concept to FNM. First, we propose a new clustering algorithm based on FNM using the concept of tolerance, which we refer to as the fuzzy non-metric model for data with tolerance. Second, we show that the proposed algorithm can handle incomplete data sets. Third, we verify the effectiveness of the proposed algorithm based on comparisons with conventional methods for incomplete data sets in some numerical examples.

Optimized aggregation function in hierarchical clustering combination

Various ensemble methods are proposed to aggregate hierarchical clusterings. These methods combine a set of hierar- chical clusterings into a single representative clustering with an improved quality. The quality of this representative hierarchical clustering intensively depends on the aggregation operator (aggregator) used in the combination. However, choosing from the large pool of aggregators is a challenging task. To facilitate this task, in this paper, we first introduce aggregator types, triangular norms and averaging operators, and then compile a list of main properties and parametric characteristics of these aggregators. An extra property which is needed in hierarchical clustering combination is also defined. Thereafter, a set of experiments is designed to elect the optimized hierarchy aggregator from the variety of these aggregators. The out coming results from the experiments are proved to be compatible with the previous applications in the field of hierarchical clustering ensembles.

Generation of brain pseudo-CTs using an undersampled, single-acquisition UTE-mDixon pulse sequence and unsupervised clustering.

MR-based pseudo-CT has an important role in MR-based radiation therapy planning and PET attenuation correction. The purpose of this study is to establish a clinically feasible approach, including image acquisition, correction, and CT formation, for pseudo-CT generation of the brain using a single-acquisition, undersampled ultrashort echo time (UTE)-mDixon pulse sequence. Nine patients were recruited for this study. For each patient, a 190-s, undersampled, single acquisition UTE-mDixon sequence of the brain was acquired (TE = 0.1, 1.5, and 2.8 ms). A novel method of retrospective trajectory correction of the free induction decay (FID) signal was performed based on point-spread functions of three external MR markers. Two-point Dixon images were reconstructed using the first and second echo data (TE = 1.5 and 2.8 ms). R2(∗) images (1/T2(∗)) were then estimated and were used to provide bone information. Three image features, i.e., Dixon-fat, Dixon-water, and R2(∗), were used for unsupervised clustering. Five tissue clusters, i.e., air, brain, fat, fluid, and bone, were estimated using the fuzzy c-means (FCM) algorithm. A two-step, automatic tissue-assignment approach was proposed and designed according to the prior information of the given feature space. Pseudo-CTs were generated by a voxelwise linear combination of the membership functions of the FCM. A low-dose CT was acquired for each patient and was used as the gold standard for comparison. The contrast and sharpness of the FID images were improved after trajectory correction was applied. The mean of the estimated trajectory delay was 0.774 μs (max: 1.350 μs; min: 0.180 μs). The FCM-estimated centroids of different tissue types showed a distinguishable pattern for different tissues, and significant differences were found between the centroid locations of different tissue types. Pseudo-CT can provide additional skull detail and has low bias and absolute error of estimated CT numbers of voxels (-22 ± 29 HU and 130 ± 16 HU) when compared to low-dose CT. The MR features generated by the proposed acquisition, correction, and processing methods may provide representative clustering information and could thus be used for clinical pseudo-CT generation.