Density Peaks Clustering Algorithm Research Articles

Density decay graph-based density peak clustering

In 2014, Rodriguez and Laio proposed a famous clustering algorithm based on a fast search and find density peaks dubbed as DPC (Rodriguez and Laio, 2014). DPC has been widely used in many fields because of its simplicity and effectiveness. However, DPC has two obvious drawbacks. First, initial cluster centers must be manually selected from the decision graph, which is extremely difficult and even impossible in some cases. Second, the result of DPC is affected by the so called “chain reaction” problem. To overcome these two drawbacks, we propose a density decay graph-based density peak clustering (DGDPC) algorithm. The key to DGDPC is the concept of density decay graph, which is inspired by the decay phenomenon (a common phenomenon in nature). In our algorithm, we form initial clusters according to density decay graphs and then merge clusters based on a simple method. As a result, there is no need to manually select cluster centers and the chain reaction problem is alleviated. Although DGDPC introduces an additional parameter m, m is robust and easy to determine in advance. Experiments on 10 synthetic datasets and 10 real-world datasets show that our algorithm outperforms DPC, DGB (Wu and Wilamowski, 2016), K-means (MacQueen et al., 1967), DBSCAN (Ester et al., 1996), and Single-link (Murtagh and Contreras, 2012) in most cases.

Non-intrusive load monitoring using factorial hidden markov model based on adaptive density peak clustering

With the goal of achieving carbon neutrality, the technology of Non-Intrusive Load Monitoring (NILM) has gained widespread attention as an efficient energy-saving way. Hidden Markov Model (HMM) based methods are popular in the field of NILM, yet the traditional HMM-based methods need prior knowledge of the appliance’s working states. In this paper, we propose an Adaptive Density Peak Clustering (ADPC) algorithm that could automatically determine the working states of appliance based on its power consumption. Then we combine the ADPC and Factorial Hidden Markov Model (FHMM) to create an Adaptive Density Peak Clustering-Factorial Hidden Markov Model (ADPC-FHMM), which reduces the dependence of prior information and is more applicable in real world scenarios. Case studies are conducted on two publicly available datasets, and the results show that the proposed model outperforms its counterparts on the metrics of Accuracy, F-measure and MAE.

Input data selection for daily traffic flow forecasting through contextual mining and intra-day pattern recognition

There is a large amount of literature about the traffic flow forecasting and most existing studies focus on prediction algorithm itself. However, how to select the appropriate historical data as input is also vital for the prediction task, while such studies are limited. This paper aims to cover this gap and proposes a method to select the appropriate historical data for daily traffic flow forecasting. The main idea is that some contextual factors including season, day of the week, weather, and holiday, influence the daily traffic flow pattern, and we select historical days with the similar pattern to the target day as the training data for prediction algorithm. The method consists of three steps: first, the similarities for traffic flow series between any two days are measured by Dynamic Time Warping, and then historical days are divided into different groups using a density-peak clustering algorithm; Second, the contextual factors are sorted by Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) using the clustering results, and their degrees of importance are transformed into weights in order to better measure the degrees of similarity between the clustered groups of days and the target day; third, one clustered group of historical data is selected based on the weighted degree of similarity and this group is used as the input for the prediction algorithm. At last, the benefits of the new method are discussed based on a Seattle case study, which illustrates that the proposed approach has higher prediction accuracy and stability across various prediction algorithms.

Neural network in sports cluster analysis

In the era of rapid development of the Internet, various types of data in daily life are becoming more and more important, as are people's sports data. How to collect and store these massive exercise data and how to extract the user's exercise habits from these data are of great significance for improving people's exercise enthusiasm. This article mainly studies the application of the network in the cluster analysis of sports. This paper proposes a combination of a neural network-based sports data analysis model and a density peak clustering algorithm for unsupervised dimensionality reduction of high-dimensional data. We design both the encoder and the decoder with a three-layer fully connected neural network structure. The encoder extracts the characteristics of the sample data, and then, the decoder approximates the original input sample. The encoder is used to reduce the dimensionality of the high-dimensional data to the middle dimension, combined with the density peak clustering algorithm to further reduce the dimensionality, and then analyze the low-dimensional data. And set the corresponding learning rate for different data sets, the three data sets are iterated 40 times. The prediction accuracy rates of the algorithm in the three data sets are 94.1%, 90.3%, and 89.6% respectively; compared with the traditional PCA dimensionality reduction method, the method in this paper can extract data features more effectively, improve the dispersion between clusters, and have a better clustering effect. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

A Density Peak-Based Method to Detect Copy Number Variations From Next-Generation Sequencing Data.

Copy number variation (CNV) is a common type of structural variations in human genome and confers biological meanings to human complex diseases. Detection of CNVs is an important step for a systematic analysis of CNVs in medical research of complex diseases. The recent development of next-generation sequencing (NGS) platforms provides unprecedented opportunities for the detection of CNVs at a base-level resolution. However, due to the intrinsic characteristics behind NGS data, accurate detection of CNVs is still a challenging task. In this article, we propose a new density peak-based method, called dpCNV, for the detection of CNVs from NGS data. The algorithm of dpCNV is designed based on density peak clustering algorithm. It extracts two features, i.e., local density and minimum distance, from sequencing read depth (RD) profile and generates a two-dimensional data. Based on the generated data, a two-dimensional null distribution is constructed to test the significance of each genome bin and then the significant genome bins are declared as CNVs. We test the performance of the dpCNV method on a number of simulated datasets and make comparison with several existing methods. The experimental results demonstrate that our proposed method outperforms others in terms of sensitivity and F1-score. We further apply it to a set of real sequencing samples and the results demonstrate the validity of dpCNV. Therefore, we expect that dpCNV can be used as a supplementary to existing methods and may become a routine tool in the field of genome mutation analysis.

A method for mixed data classification base on RBF-ELM network

The classification tasks for numerical or categorical data have been well developed. However, the data collected in the real world are frequently the mixed type containing numerical and categorical values, and how to classify the mixed data quickly and efficiently is a critical yet challenging task. Existing classification models for mixed data usually treat the mixed data processing and subsequent classification as two independent phases, without considering their compatibility. By fusing the mixed data processing into a classification algorithm, this paper proposes an extended version of RBF-ELM (Radial Basis Function-Extreme Learning Machine), a Mixed Data RBF-ELM method (MD-RBF-ELM for short), which can achieve direct, fast, and efficient classification for mixed data. Specifically, a distance metric method for mixed data is firstly designed to calculate the distances between the input data and the RBF centers, and then these distances are used to train the network structure and weights of MD-RBF-ELM, thereby realizing the fusion of data processing with model learning. In addition, to alleviate the problem of MD-RBF-ELM’s unstable performance caused by randomly selecting the RBF centers, we propose an improved density peak clustering algorithm and use it to select the optimal RBF centers automatically and adaptively. Extensive experimental results on 34 data sets demonstrate that MD-RBF-ELM significantly enhances the classification performance (increasing 2.37% for F1-score, up to 14/34 for the number of best results, and reaching 2.4/8 for the averaged ranks), compared with seven state-of-the-art competitors.

Density peaks clustering based on geodetic distance and dynamic neighbourhood

Density peaks clustering algorithm uses Euclidean distance as a measure of similarity between the samples and it can achieve a good clustering effect when processing the manifold datasets. Utilising this feature, we propose a density peaks clustering algorithm based on geodetic distance and dynamic neighbourhood. This new algorithm measures the similarity between the samples by using geodetic distance, and the number of neighbours K is dynamically adjusted according to the spatial distribution of samples for geodetic distance computation. By choosing geodetic distance as the similarity measure, the problems of manifold dataset clustering can be easily solved, and the clustering is made more effective when the sparse clusters and dense clusters co-exist. The new algorithm was then compared against the other five clustering algorithms on six synthetic datasets and ten real-world datasets. The experiments showed that the proposed algorithm not only outperformed the other conventional algorithms on manifold datasets, but also achieved a very good clustering effect on multi-scale, cluttered and intertwined datasets.

An improved density peaks clustering algorithm based on CURE

As a new density-based clustering algorithm, clustering by fast search and find of Density Peaks (DP) algorithm regards each density peak as a potential clustering center when dealing with a single cluster with multiple density peaks, therefore it is difficult to determine the correct number of clusters in the data set. To solve this problem, a mixed density peak clustering algorithm namely C-DP was proposed. Firstly, the density peak points were considered as the initial clustering centers and the dataset was divided into sub-clusters. Then, learned from the Clustering Using Representatives algorithm (CURE), the scattered representative points were selected from the sub-clusters, the clusters of the representative point pairs with the smallest distance were merged, and a parameter contraction factor was introduced to control the shape of the clusters. The experimental results show that the C-DP algorithm has better clustering effect than the DP algorithm. The comparison of the F-measure Index shows that the C-DP algorithm improves the accuracy of clustering when datasets contain multiple density peaks in a single cluster.

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.

A Partial Discharge Localization Method in Transformers Based on Linear Conversion and Density Peak Clustering

The detection of partial discharge (PD) is a crucial method to evaluate the insulation status of transformers. The main difficulties of the current localization algorithms are the complexity of the solution and sensitivity to time delay errors. This article proposes a PD localization method in transformers based on linear conversion and density peak clustering (DPC). First, to reduce the complexity of solving the localization equations, the nonlinear localization equations are transformed into linear localization equations by eliminating the second-order terms. Then, to reduce the influence of time delay errors on localization accuracy, the initial localization values are located by multiple acoustic emission (AE) sensors. Finally, the optimal PD coordinates are determined by clustering the initial location values using density peaks clustering algorithm with automatic finding centers (AFC-DPC). The experimental results show that the proposed method can improve PD localization accuracy in transformers, and the average localization error is 5.30 cm.

Density peaks clustering based on geodetic distance and dynamic neighbourhood

Density peaks clustering algorithm uses Euclidean distance as a measure of similarity between the samples and it can achieve a good clustering effect when processing the manifold datasets. Utilisin...

The DPC-Based Scheme for Detecting Selective Forwarding in Clustered Wireless Sensor Networks

Many studies have shown that clustered Wireless Sensor Networks (WSNs) have a better performance in terms of the balance of energy and lifetime. However, due to the harsh environment and open communication, the clustered WSNs are easy to be attacked. The selective forwarding attack is one of the most difficult attacks to be detected. When a malicious sensor node launches the selective forwarding attacks, it drops part of or all the data packets it received. In this paper, we propose a Noise-Based Density Peaks Clustering (NB-DPC) algorithm for detecting selective forwarding attacks. It can detect selective forwarding attacks by clustering the Cumulative Forwarding Rates (CFRs) of all sensor nodes. The NB-DPC algorithm has been improved by defining noise points specifically for identifying malicious behavior and deleting the unnecessary steps in Density Peaks Clustering (DPC) for faster detection speed. The NB-DPC has a low Missed Detection Rate (MDR) and False Detection Rate (FDR) of below 1% according to the simulation results.

Community discovery algorithm under big data: taking microblog as an example

Microblog has become a popular social media because of its short text and timely release, and its impact on society has gradually increased. In order to study the behaviour of microblog users, this paper introduced two algorithms for microblog network community division, which were community discovery algorithm based on density peak clustering and community discovery algorithm based on similarity. Then the two algorithms were simulated using MATLAB software. The data used in the experiment included the artificial network generated by LFR tool and the following information data of different users collected by taking the API interface of the microblog of a student from Computer School of Jining Normal University as the starting point by crawlers. The results demonstrated that the normalised mutual information (NMI) and the density of the community structure obtained by the two algorithms decreased, and the conductivity increased with the expansion of the scale of microblog network, and the community structure obtained by the similarity-based algorithm had higher NMI and density and lower conductivity under the same scale of micrblog network. In conclusion, the similarity-based algorithm can divide microblog network better.

An Improved Algorithm Based on Fast Search and Find of Density Peak Clustering for High‐Dimensional Data

The find of density peak clustering algorithm (FDP) has poor performance on high‐dimensional data. This problem occurs because the clustering algorithm ignores the feature selection. All features are evaluated and calculated under the same weight, without distinguishing. This will lead to the final clustering effect which cannot achieve the expected. Aiming at this problem, we propose a new method to solve it. We calculate the importance value of all features of high‐dimensional data and calculate the mean value by constructing random forest. The features whose importance value is less than 10% of the mean value are removed. At this time, we extract the important features to form a new dataset. At this time, improved t‐SNE is used for dimension reduction, and better performance will be obtained. This method uses t‐SNE that is improved by the idea of random forest to reduce the dimension of the original data and combines with improved FDP to compose the new clustering method. Through experiments, we find that the evaluation index NMI of the improved algorithm proposed in this paper is 23% higher than that of the original FDP algorithm, and 9.1% higher than that of other clustering algorithms (K‐means, DBSCAN, and spectral clustering). It has good performance in high‐dimensional datasets that are verified by experiments on UCI datasets and wireless sensor networks.

A study on Two-Stage Mixed Attribute Data Clustering Based on Density Peaks

A Two-stage clustering framework and a clustering algorithm for mixed attribute data based on density peaks and Goodall distance are proposed. Firstly, the subset of numerical attributes of the dataset is clustered, and then the result is mapped into one-dimensional categorical attribute and added to the subset of categorical attribute data. Finally, the new dataset is clustered by the density peaks clustering algorithm to obtain the final result. Experiments on three commonly used UCI datasets show that this algorithm can effectively realize mixed attribute clustering and produce better clustering results than the traditional K-prototypes algorithm do. The clustering accuracy on the Acute, Heart and Credit datasets are 17%, 24%, and 21% higher on average than that of the K-prototypes, respectively.

Underdetermined Mixed Matrix Estimation Based on DPCKFCM Algorithm

Aiming at the problem of fuzzy C-means (FCM) in the estimation of underdetermined mixing matrix, that the estimation accuracy is not high and the robustness is poor, a density peak clustering (DPC) based on density peak clustering (DPC) is proposed. Improved Kernel-based Fuzzy C-means (KFCM). The kernel function is introduced into the FCM algorithm to construct the KFCM algorithm based on the Gaussian kernel function, which can effectively overcome the influence of noise points and isolated points on the clustering results and improve the estimation accuracy of the mixed matrix; the traditional DPC algorithm is improved and merged with the KFCM algorithm, and thresholds are set for the local density and high-density distance to achieve the initial clustering center of the KFCM algorithm and the automatic determination of the number of cluster centers improves the robustness of the algorithm. Experimental results show that the algorithm has greatly improved the estimation accuracy and robustness of the underdetermined mixed matrix.

A fast density peaks clustering algorithm with sparse search

Given a large unlabeled set of complex data, how to efficiently and effectively group them into clusters remains a challenging problem. Density peaks clustering (DPC) algorithm is an emerging algorithm, which identifies cluster centers based on a decision graph. Without setting the number of cluster centers, DPC can effectively recognize the clusters. However, the similarity between every two data points must be calculated to construct a decision graph, which results in high computational complexity. To overcome this issue, we propose a fast sparse search density peaks clustering (FSDPC) algorithm to enhance the DPC, which constructs a decision graph with fewer similarity calculations to identify cluster centers quickly. In FSDPC, we design a novel sparse search strategy to measure the similarity between the nearest neighbors of each data points. Therefore, FSDPC can enhance the efficiency of the DPC while maintaining satisfactory results. We also propose a novel random third-party data point method to search the nearest neighbors, which introduces no additional parameters or high computational complexity. The experimental results on synthetic datasets and real-world datasets indicate that the proposed algorithm consistently outperforms the DPC and other state-of-the-art algorithms.

Editorial for special issue on security, trust, and privacy in internet of things: Challenges and solutions

Editorial for special issue on security, trust, and privacy in internet of things: Challenges and solutions

Fast Searching Density Peak Clustering Algorithm Based on Shared Nearest Neighbor and Adaptive Clustering Center

The clustering analysis algorithm is used to reveal the internal relationships among the data without prior knowledge and to further gather some data with common attributes into a group. In order to solve the problem that the existing algorithms always need prior knowledge, we proposed a fast searching density peak clustering algorithm based on the shared nearest neighbor and adaptive clustering center (DPC-SNNACC) algorithm. It can automatically ascertain the number of knee points in the decision graph according to the characteristics of different datasets, and further determine the number of clustering centers without human intervention. First, an improved calculation method of local density based on the symmetric distance matrix was proposed. Then, the position of knee point was obtained by calculating the change in the difference between decision values. Finally, the experimental and comparative evaluation of several datasets from diverse domains established the viability of the DPC-SNNACC algorithm.

Distributed Density Peaks Clustering Revisited

Density Peaks (DP) Clustering organizes data into clusters by finding peaks in dense regions. This involves computing density ( <inline-formula><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> ) and distance ( <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> ) of every point. As such, though DP has been very effective in producing high quality clusters, their complexity is O( <inline-formula><tex-math notation="LaTeX">$N^2$</tex-math></inline-formula> ) where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of data points. In this paper, we propose a fast distributed density peaks clustering algorithm, FDDP, based on the z-value index. In FDDP, we first employ the z-value index to map multi-dimensional data points into one dimensional space, and then range-partition the data according to the z-value to balance the load across the processing nodes. We ensure minimal overlapping range to handle computations at the boundary points. We also propose FC, an efficient algorithm that employs a forward computing strategy to calculate <inline-formula><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> linearly. Additionally, we propose another algorithm, CB, which uses a caching and efficient searching strategy to compute <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> . Moreover, FDDP is able to reduce the time complexity from <inline-formula><tex-math notation="LaTeX">$O(N^2)$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$O(N\cdot log(N))$</tex-math></inline-formula> . We provide a theoretical analysis of FDDP and evaluated FDDP empirically. Our experimental results show that FDDP outperforms the state-of-the-art algorithms significantly.