Density Peaks Clustering Method Research Articles

Hybrid Clustering Algorithm Based on Improved Density Peak Clustering

In the era of big data, unsupervised learning algorithms such as clustering are particularly prominent. In recent years, there have been significant advancements in clustering algorithm research. The Clustering by Density Peaks algorithm is known as Clustering by Fast Search and Find of Density Peaks (density peak clustering). This clustering algorithm, proposed in Science in 2014, automatically finds cluster centers. It is simple, efficient, does not require iterative computation, and is suitable for large-scale and high-dimensional data. However, DPC and most of its refinements have several drawbacks. The method primarily considers the overall structure of the data, often resulting in the oversight of many clusters. The choice of truncation distance affects the calculation of local density values, and varying dataset sizes may necessitate different computational methods, impacting the quality of clustering results. In addition, the initial assignment of labels can cause a ‘chain reaction’, i.e., if one data point is incorrectly labeled, it may lead to more subsequent data points being incorrectly labeled. In this paper, we propose an improved density peak clustering method, DPC-MS, which uses the mean-shift algorithm to find local density extremes, making the accuracy of the algorithm independent of the parameter dc. After finding the local density extreme points, the allocation strategy of the DPC algorithm is employed to assign the remaining points to appropriate local density extreme points, forming the final clusters. The robustness of this method in handling uncertain dataset sizes adds some application value, and several experiments were conducted on synthetic and real datasets to evaluate the performance of the proposed method. The results show that the proposed method outperforms some of the more recent methods in most cases.

Improved kernel density peaks clustering for plant image segmentation applications

Abstract In order to better solve the shortcomings of the k-means clustering method and density peaks clustering (DPC) method in agricultural image segmentation, this work proposes a method to divide points in a high-dimensional space, and a clustering method is obtained to divide crops and soil. In the process of assigning points in the DPC method, if a point is divided incorrectly, a series of points may be assigned to a cluster that is not related to it. In response to this problem, this study uses the decision graph to select the centroids, and uses Gaussian kernel to map the data to the high-dimensional space, each centroid searches for the most relevant points in the high-dimensional space until a temporary boundary point is found to stop the first assignment strategy, and then the points that are not clustered are assigned to the correct cluster to complete the clustering. The experimental results show that the proposed method has a better clustering effect through experiments on multiple artificial datasets and UCI datasets, compared with other clustering methods, and finally applied to plant image segmentation.

An improved hierarchical clustering method based on the k‐NN and density peak clustering

AbstractClustering is one of the most prevalent and important data mining algorithms ever developed. Currently, most clustering methods are divided into distance‐based and density‐based. In 2014, the fast search and find of density peaks clustering method was proposed, which is simple and effective and has been extensively applied in several research domains. However, the original version requires manually assigning a cut‐off distance and selecting core points. Therefore, this article improves the density peak clustering method from two aspects. First, the Gaussian kernel is substituted with a k‐nearest neighbors method to calculate local density. This is important as compared with selecting a cut‐off distance, calculating the k‐value is easier. Second, the core points are automatically selected, unlike the original method that manually selects the core points regarding local density and distance distribution. Given that users' selection influences the clustering result, the proposed automatic core point selection strategy overcomes the human interference problem. Additionally, in the clustering process, the proposed method reduces the influence of manually assigned parameters.

A fair consensus adjustment mechanism for large-scale group decision making in term of Gini coefficient

With social media and e-democracy development, decision-making environments and problems have become increasingly complex. Traditional group decision-making, including a small number of decision makers, cannot deal with many practical decision-making problems. Large-scale group decision-making has received extensive attention as an efficient measure to address this issue. This paper proposes a two-stage optimization consensus mechanism for large-scale group decision-making by the Gini coefficient, which considers both the consensus among decision makers’ opinions and the fairness of consensus adjustment. First, we introduce an improved density peak clustering method to cluster decision makers into subgroups that can avoid different clustering centers being too close. Then, we define the subgroups' weights by the silhouette coefficient, the subgroup judgment distance, and their sizes. Respecting the importance of minority opinions, we design a new method to identify and adjust the weights of the minority opinions, which considers more aspects than previous ones. Further, we use the Gini coefficient to measure the equity of consensus adjustment of the group and subgroup. Moreover, we present a two-stage Gini coefficient-based consensus mechanism to obtain the adjusted consensus individual decision matrices, which can ensure the minimization and fairness of consensus adjustment and allocation under the set constraints. Based on these results, we give a new large-scale group decision-making method. Notably, it is the first method that fully considers the opinions of minor subgroups and the fairness of allocation results. These characteristics are essential in decision-making problems such as resource allocation and urban public construction. Finally, we show the utility and validity of the new method through a case study and make the comparative analysis from numerical and principle aspects.

Constrained Density Peak Clustering

Clustering is a commonly used tool for discovering knowledge in data mining. Density peak clustering (DPC) has recently gained attention for its ability to detect clusters with various shapes and noise, using just one parameter. DPC has shown advantages over other methods, such as DBSCAN and K-means, but it struggles with datasets that have both high and low-density clusters. To overcome this limitation, the paper introduces a new semi-supervised DPC method that improves clustering results with a small set of constraints expressed as must-link and cannot-link. The proposed method combines constraints and a k-nearest neighbor graph to filter out peaks and find the center for each cluster. Constraints are also used to support label assignment during the clustering procedure. The efficacy of this method is demonstrated through experiments on well-known data sets from UCI and benchmarked against contemporary semi-supervised clustering techniques.

A Fast Density Peak Clustering Method for Power Data Security Detection Based on Local Outlier Factors

The basic work of power data research is anomaly detection. It is necessary to find a method suitable for processing current power system data. Research proposes an algorithm of fast density peak clustering with Local Outlier Factor (LOF). The algorithm has poor performance in processing datasets with irregular shapes and significant local density changes, and has the disadvantage of strong dependence on truncation distance. This study provides the decision rules for outliers incorporating the idea of LOF. The improved algorithm can fully consider the characteristics of power data and reduce the dependence on truncation distance. In anomaly detection based on the simulation of real power data, the classification accuracy of the improved CFSFDP algorithm is 4.87% higher than that of the traditional algorithm, and the accuracy rate is 97.41%. The missed and false detection rates of the LOF-CFSFDP algorithm are decreased by 2.23% and 2.64%, respectively, compared to the traditional algorithm, and it is ultimately able to reach rates of 1.26% and 1.33%. These results indicate that the algorithm proposed in this study can better describe the characteristics of power data, making the features of outliers and cluster center points more obvious.

Intermittent Fault Recognition of Analog Circuits in the Presence of Outliers via Density Peak Clustering With Adaptive Weighted Distance

Intermittent faults (IF) are the main cause of analog circuit failures, which are short lived and repeatable. Since IF sample labels are difficult to obtain, unsupervised cluster recognition is an important method to help experts analyze potential classes of IFs. However, outliers generated by noise can affect the recognition of IFs. In this paper, an improved density peak clustering method is proposed, which enhances the fault recognition performance in terms of both distance and outlier detection. First, an adaptive weighted distance is proposed, which can give different distance weights according to the similarity between two samples. Thus, the outliers have a greater distance from the IF samples and reduce the influence of the outliers on the IF recognition. Second, a new outlier detection strategy is used to improve the density peak clustering (DPC) algorithm. The new strategy enhances outlier detection and prevents low-density clusters from being misdetected as outliers, thus further reducing the impact of outliers on IF recognition. Finally, the proposed method is applied to two typical analog filter circuits. The results show that this method can effectively recognize IFs in analog circuits.

Build Network Intrusion Detection System based on combination of Fractal Density Peak Clustering and Artificial Neural Network

Imbalanced data poses a serious problem in intrusion detection systems. In this article, we propose a network intrusion detection system based on fractal density peak clustering and an artificial neural network (FD-ANN). The proposed detection system consists of three parts: data clustering based on the density-peak clustering (DPC) method, using the fractal concept as a membership weight of all data to the cluster, and a neural network to classify the data. The DPC method uses categorization of the tare data into subgroups with strongly correlated attributes to reduce the size of the training data and the imbalance of the sample. Each subgroup has its neural network to train the data. Based on fractal membership weights, the output of all classifiers of the sub-neural networks is combined using the aggregation function. The benchmarks of this model are based on the data sets NSL-KDD and UNSW-NB15. The proposed solution outperforms other known classification approaches in terms of overall accuracy, recall, precision, and F1 score.

Fault Diagnosis of Mine Ventilator Bearing Based on Improved Variational Mode Decomposition and Density Peak Clustering

The mine ventilator plays a role in protecting the life safety of underground workers, which is very significant to the production and development of coal mines. In total, 70% of ventilator failures are mechanical failures, and bearing failures are the most likely to occur in mechanical failures, which are also difficult to find. In order to identify fan bearing faults accurately, this paper proposes a fault diagnosis method based on improved variational mode decomposition and density peak clustering. First, the variational mode decomposition’s modal number K and secondary penalty factor α are chosen employing the improved sparrow optimization process. The bearing vibration signal is decomposed by the variational mode decomposition algorithm with optimized parameters. To create the characteristic vector, the multi-scale permutation entropy of the fourth order intrinsic mode function is determined. Then, the characteristic matrix is dimensionally reduced by kernel principal component analysis, and the two-dimensional matrix after dimensionality reduction is divided by density peak clustering method to find the clustering center of the training sample features. Lastly, the membership degree is assessed using the normalized clustering distance between the characteristic matrix of the test sample and the cluster center of the training sample. The accuracy of bearing fault identification on the self-constructed experimental platform can reach 100%, which verifies the effectiveness and potential of the proposed method.

Microfeature Segmentation Algorithm for Biological Images Using Improved Density Peak Clustering.

To address the problem of low precision in feature segmentation of biological images with large noise, a microfeature segmentation algorithm for biological images using improved density peak clustering was proposed. First, the center pixel and edge information of a biological image were obtained to remove some redundant information. The three-dimensional space of the image is constructed, and the coordinate system is used to describe every superpixel of the biological image. Second, the image symmetry and reversibility are used to obtain the stopping position of pixels, other adjacent points are used to obtain the current color and shape information, and more vectors are used to express the density to complete the image pretreatment. Finally, the improved density peak clustering method is used to cluster the image, and the pixels completed by clustering and the remaining pixels are evenly distributed into the space to segment the image so as to complete the microfeature segmentation of the biological image based on the improved density peak clustering method. The results show that the proposed algorithm improves the segmentation efficiency, segmentation integrity rate, and segmentation accuracy. The time consumed by the proposed biological image microfeature segmentation algorithm is always less than 2 minutes, and the segmentation integrity rate can reach more than 90%. Furthermore, the proposed algorithm can reduce the missing condition and the noise of the segmented image and improve the image feature segmentation effect.

An Improved Clustering Algorithm Based on Density Peak and Nearest Neighbors

Aiming at the problems that the initial cluster centers are randomly selected and the number of clusters is manually determined in traditional clustering algorithm, which results in unstable clustering results, we propose an improved clustering algorithm based on density peak and nearest neighbors. Firstly, an improved density peak clustering method is proposed to optimize the cutoff distance and local density of data points. It avoids that random selection of initial cluster centers is easy to fall into the local optimal solution. Furthermore, a K-value selection method is presented to choose the optimal number of clusters, which is determined by the sum of the squared errors within the clusters. Finally, we employ the idea of the K-nearest neighbors to carry out the assignment for outliers. Experiments on the UCI real data sets indicate that our proposed algorithm can achieve better clustering results compared with several known algorithms.

A Fast Density Peak Clustering Method with Autoselect Cluster Centers

Aiming at density peaks clustering needs to manually select cluster centers, this paper proposes a fast new clustering method with auto-select cluster centers. Firstly, our method groups the data and marks each group as core or boundary groups according to its density. Secondly, it determines clusters by iteratively merging two core groups whose distance is less than the threshold and selects the cluster centers at the densest position in each cluster. Finally, it assigns boundary groups to the cluster corresponding to the nearest cluster center. Our method eliminates the need for the manual selection of cluster centers and improves clustering efficiency with the experimental results.

3D Shape Segmentation Using Soft Density Peak Clustering and Semi-Supervised Learning

Shape segmentation plays a vital role in shape analysis. Recent research uses fully-supervised learning methods to achieve state-of-the-art performance. However, acquiring fully-labeled training data is usually an extremely expensive process. In this paper, we present a novel semi-supervised algorithm for 3D shape segmentation. In our method, users are only required to locate several seed faces with a very simple interaction by using our soft density peak clustering method. Our method can automatically learn the required label information and produce satisfactory segmentation results with our novel optimization model. Various experimental results show that the presented method can achieve superior segmentation performance over previous unsupervised methods and comparable performance to the fully-supervised methods.

Damage Pattern Recognition and Crack Propagation Prediction for Crumb Rubber Concrete Based on Acoustic Emission Techniques

In this study, the clustering method of the concrete matrix rupture and rubber fracture damages as well as the prediction of the ultimate load of crumb rubber concrete using the acoustic emission (AE) technique were investigated. The loading environment of the specimens was a four-point bending load. Six clustering methods including k-means, fuzzy c-means (FCM), self-organizing mapping (SOM), Gaussian mixture model (GMM), hierarchical model, and density peak clustering method were analyzed; the results illustrated that the density peak clustering has the best performance. Next, the optimal clustering algorithm was used to cluster AE signals so as to study the evolution behavior of different damage modes, and the ultimate load of crumb rubber concrete was predicted by an artificial neural network. The results indicated that the combination of AE techniques and appropriate clustering methods such as the density peak clustering method and the artificial neural network could be used as a practical tool for structural health monitoring of crumb rubber concrete.

An automatic clustering algorithm based on the density-peak framework and Chameleon method

• The proposed method only needs a single discrete input parameter. • The proposed method has a robust performance in the different density scenario. • The proposed method can automatically detect the number of clusters. • We adapt the cluster stability for our method and find a new way to calculate it. The density-peak clustering (DPC) method (Rodriguez and Laio, 2014) clusters the data efficiently by fast searching density peaks. Recently, an improved DPC algorithm named 3DC method (Liang and Chen, 2016) was proposed for automatically detecting the correct structure of the clusters. However, it is difficult to select correct parameters for the DPC and 3DC methods and the local property of data set can’t be revealed due to their global density assumption in some scenarios. To overcome this drawback, the K-nearest neighbor (KNN) framework is adapted for defining the density of the DPC method. Nevertheless, such KNN-based methods can’t automatically detect the number of the clusters compared with the 3DC method. In this paper, an automatic clustering method is proposed, which needs only a discrete input parameter. Meanwhile, by utilizing the cluster stability for the Chameleon framework, the proposed method can automatically detect the correct structure of the clusters. The experimental results on the synthetic and real world data demonstrate that the proposed method has a more robust performance. Besides, the proposed method is robust to the choices of the input parameter.

QuantifyPoly(A): reshaping alternative polyadenylation landscapes of eukaryotes with weighted density peak clustering.

The dynamic choice of different polyadenylation sites in a gene is referred to as alternative polyadenylation, which functions in many important biological processes. Large-scale messenger RNA 3' end sequencing has revealed that cleavage sites for polyadenylation are presented with microheterogeneity. To date, the conventional determination of polyadenylation site clusters is subjective and arbitrary, leading to inaccurate annotations. Here, we present a weighted density peak clustering method, QuantifyPoly(A), to accurately quantify genome-wide polyadenylation choices. Applying QuantifyPoly(A) on published 3' end sequencing datasets from both animals and plants, their polyadenylation profiles are reshaped into myriads of novel polyadenylation site clusters. Most of these novel polyadenylation site clusters show significantly dynamic usage across different biological samples or associate with binding sites of trans-acting factors. Upstream sequences of these clusters are enriched with polyadenylation signals UGUA, UAAA and/or AAUAAA in a species-dependent manner. Polyadenylation site clusters also exhibit species specificity, while plants ones generally show higher microheterogeneity than that of animals. QuantifyPoly(A) is broadly applicable to any types of 3' end sequencing data and species for accurate quantification and construction of the complex and dynamic polyadenylation landscape and enables us to decode alternative polyadenylation events invisible to conventional methods at a much higher resolution.

A Weakly Supervised Gas-Path Anomaly Detection Method for Civil Aero-Engines Based on Mapping Relationship Mining of Gas-Path Parameters and Improved Density Peak Clustering.

Gas-path anomalies account for more than 90% of all civil aero-engine anomalies. It is essential to develop accurate gas-path anomaly detection methods. Therefore, a weakly supervised gas-path anomaly detection method for civil aero-engines based on mapping relationship mining of gas-path parameters and improved density peak clustering is proposed. First, the encoder-decoder, composed of an attention mechanism and a long short-term memory neural network, is used to construct the mapping relationship mining model among gas-path parameters. The predicted values of gas-path parameters under the restriction of mapping relationships are obtained. The deviation degree from the original values to the predicted values is regarded as the feature. To force the extracted features to better reflect the anomalies and make full use of weakly supervised labels, a weakly supervised cross-entropy loss function under extreme class imbalance is deployed. This loss function can be combined with a simple classifier to significantly improve the feature extraction results, in which anomaly samples are more different from normal samples and do not reduce the mining precision. Finally, an anomaly detection method is deployed based on improved density peak clustering and a weakly supervised clustering parameter adjustment strategy. In the improved density peak clustering method, the local density is enhanced by K-nearest neighbors, and the clustering effect is improved by a new outlier threshold determination method and a new outlier treatment method. Through these settings, the accuracy of dividing outliers and clustering can be improved, and the influence of outliers on the clustering process reduced. By introducing weakly supervised label information and automatically iterating according to clustering and anomaly detection results to update the hyperparameter settings, a weakly supervised anomaly detection method without complex parameter adjustment processes can be implemented. The experimental results demonstrate the superiority of the proposed method.

DP-GMM clustering-based ensemble learning prediction methodology for dam deformation considering spatiotemporal differentiation

The deformation behavior can effectively reflect the health status of a dam, which can suffer from dynamic and time-varying loading modes and material properties, exhibiting distinct spatiotemporal differentiation. The conventional dam health evaluations, however, focus on the displacement regularity of local monitoring points, ignoring the spatiotemporal diversity in deformation behavior, and thus cannot truly reflect the status of the entire dam. Moreover, most of the existing displacement predictions are conducted on a single-algorithm machine-learning-based model, which focuses on single-task regression and disregards the potential cross-relatedness among the deformation in adjacent areas of the dam, showing less competitiveness in complex input–output relationship learning for various spatiotemporal conditions. For more reliable deformation forecasting, an integrated displacement prediction methodology considering spatiotemporal differentiation is proposed based on the spatiotemporal clustering and machine learning algorithms, in which the minimum-density-entropy-optimized density peaks clustering method is embedded with Gaussian-mixture-model-based clustering to achieve the reliable spatiotemporal differentiation identification of dam behavior and a multioutput ensemble learning framework coupled with the extreme learning machine and support vector machine is designed to capture the complex mapping from environmental factors to deformation, considering the cross-relatedness and spatiotemporal diversity. Moreover, a synchronous optimization strategy based on improved grey wolf optimization is embedded to enhance the performance. Hence, the final deformation behavior is forecasted by the ensemble learning of various data features and mapping rules. Taking the displacement observations of an actual dam as an example, the results show that the proposed methodology achieves excellent performance in dam behavior forecasting.

Bearing Fault Diagnosis Method Based on Ensemble Composite Multi-Scale Dispersion Entropy and Density Peaks Clustering

For bearing fault diagnosis, how to effectively extract informative fault information and accurately diagnose faults is still a key problem. To this end, this study proposes a novel bearing fault diagnosis approach based on ensemble composite multi-scale dispersion entropy (ECMDE), local preserving projections and density peaks clustering. Specifically, ECMDEs are developed to capture multi-scale fault features from the raw vibration signals. The goal of ECMDEs is to synthesize different kinds of composite multi-scale dispersion entropies to find more effective fault information. Subsequently, the local preserving projections method is utilized to reduce high-dimensional feature set and extract the effective fault information. Finally, the reduced features are fed into the density peaks clustering method to obtain the fault diagnosis results. Two experimental cases and extensive comparisons are applied to validate the effectiveness and noise robustness of the proposed method. Experimental results demonstrate that the proposed method is capable to reliably extract effective fault information of raw vibration signals and accurately diagnose bearing faults even under low signal-to-noise ratio conditions.

Peak-Graph-Based Fast Density Peak Clustering for Image Segmentation

Fuzzy c-means (FCM) algorithm as a traditional clustering algorithm for image segmentation cannot effectively preserve local spatial information of pixels, which leads to poor segmentation results with inconsistent regions. For the remedy, superpixel technologies are applied, but spatial information preservation highly relies on the quality of superpixels. Density peak clustering algorithm (DPC) can reconstruct spatial information of arbitrary-shaped clusters, but its high time complexity $O(n^2)$ and unrobust allocation strategy decrease its applicability for image segmentation. Herein, a fast density peak clustering method (PGDPC) based on the kNN distance matrix of data with time complexity $O(nlog(n))$ is proposed. By using the peak-graph-based allocation strategy, PGDPC is more robust in the reconstruction of spatial information of various complex-shaped clusters, so it can rapidly and accurately segment images into high-consistent segmentation regions. Experiments on synthetic datasets, real and Wireless Capsule Endoscopy (WCE) images demonstrate that PGDPC as a fast and robust clustering algorithm is applicable to image segmentation.