Improved Density Peak Clustering Algorithm Research Articles

An Improved Density Peaks Clustering Algorithm Based On Density Ratio

Abstract Density peaks clustering (DPC) is a relatively new density clustering algorithm. It is based on the idea that cluster centers always have relatively high local densities and are relatively far from the points with higher densities. With the aforementioned idea, a decision graph can be drawn, and cluster centers will be chosen easily with the aid of the decision graph. However, the algorithm has its own weaknesses. Because the algorithm calculates local density and allocates points based on the distances between certain points, the algorithm has difficulty in classifying points into proper groups with varying densities or nested structures. This paper proposes an improved density peaks clustering algorithm called Dratio-DPC to overcome this weakness. First, Dratio-DPC adjusts the original local density with a coefficient calculated with the density ratio. Second, Dratio-DPC takes density similarity into consideration to calculate the distances between one point and other points with higher local densities. We design and perform experiments on different benchmark datasets and compare the clustering results of Dratio-DPC, traditional clustering algorithms and three improved DPC algorithms. Comparison results show that Dratio-DPC is effective and applicable to a wider range of scenarios.

User profiling for Chinese super-new generation wine consumers based on improved density peak clustering algorithm

PurposeFor a better understanding of the preferences and differences of young consumers in emerging wine markets, this study aims to propose a clustering method to segment the super-new generation wine consumers based on their sensitivity to wine brand, origin and price and then conduct user profiles for segmented consumer groups from the perspectives of demographic attributes, eating habits and wine sensory attribute preferences.Design/methodology/approachWe first proposed a consumer clustering perspective based on their sensitivity to wine brand, origin and price and then conducted an adaptive density peak and label propagation layer-by-layer (ADPLP) clustering algorithm to segment consumers, which improved the issues of wrong centers' selection and inaccurate classification of remaining sample points for traditional DPC (DPeak clustering algorithm). Then, we built a consumer profile system from the perspectives of demographic attributes, eating habits and wine sensory attribute preferences for segmented consumer groups.FindingsIn this study, 10 typical public datasets and 6 basic test algorithms are used to evaluate the proposed method, and the results showed that the ADPLP algorithm was optimal or suboptimal on 10 datasets with accuracy above 0.78. The average improvement in accuracy over the base DPC algorithm is 0.184. As an outcome of the wine consumer profiles, sensitive consumers prefer wines with medium prices of 100–400 CNY and more personalized brands and origins, while casual consumers are fond of popular brands, popular origins and low prices within 50 CNY. The wine sensory attributes preferred by super-new generation consumers are red, semi-dry, semi-sweet, still, fresh tasting, fruity, floral and low acid.Practical implicationsYoung Chinese consumers are the main driver of wine consumption in the future. This paper provides a tool for decision-makers and marketers to identify the preferences of young consumers quickly which is meaningful and helpful for wine marketing.Originality/valueIn this study, the ADPLP algorithm was introduced for the first time. Subsequently, the user profile label system was constructed for segmented consumers to highlight their characteristics and demand partiality from three aspects: demographic characteristics, consumers' eating habits and consumers' preferences for wine attributes. Moreover, the ADPLP algorithm can be considered for user profiles on other alcoholic products.

Soft Sensor Modeling Method for the Marine Lysozyme Fermentation Process Based on ISOA-GPR Weighted Ensemble Learning.

Due to the highly nonlinear, multi-stage, and time-varying characteristics of the marine lysozyme fermentation process, the global soft sensor models established using traditional single modeling methods cannot describe the dynamic characteristics of the entire fermentation process. Therefore, this study proposes a weighted ensemble learning soft sensor modeling method based on an improved seagull optimization algorithm (ISOA) and Gaussian process regression (GPR). First, an improved density peak clustering algorithm (ADPC) was used to divide the sample dataset into multiple local sample subsets. Second, an improved seagull optimization algorithm was used to optimize and transform the Gaussian process regression model, and a sub-prediction model was established. Finally, the fusion strategy was determined according to the connectivity between the test samples and local sample subsets. The proposed soft sensor model was applied to the prediction of key biochemical parameters of the marine lysozyme fermentation process. The simulation results show that the proposed soft sensor model can effectively predict the key biochemical parameters with relatively small prediction errors in the case of limited training data. According to the results, this model can be expanded to the soft sensor prediction applications in general nonlinear systems.

An Improved Density Peak Clustering Algorithm Based on Chebyshev Inequality and Differential Privacy

This study aims to improve the quality of the clustering results of the density peak clustering (DPC) algorithm and address the privacy protection problem in the clustering analysis process. To achieve this, a DPC algorithm based on Chebyshev inequality and differential privacy (DP-CDPC) is proposed. Firstly, the distance matrix is calculated using cosine distance instead of Euclidean distance when dealing with high-dimensional datasets, and the truncation distance is automatically calculated using the dichotomy method. Secondly, to solve the difficulty in selecting suitable clustering centers in the DPC algorithm, statistical constraints are constructed from the perspective of the decision graph using Chebyshev inequality, and the selection of clustering centers is achieved by adjusting the constraint parameters. Finally, to address the privacy leakage problem in the cluster analysis, the Laplace mechanism is applied to introduce noise to the local density in the process of cluster analysis, enabling the privacy protection of the algorithm. The experimental results demonstrate that the DP-CDPC algorithm can effectively select the clustering centers, improve the quality of clustering results, and provide good privacy protection performance.

An improved density peaks clustering algorithm based on k nearest neighbors and turning point for evaluating the severity of railway accidents

The timely and scientific assessment of railway accident severity can provide effective support for making a suitable rescue plan. This paper proposes an improved density peaks clustering algorithm based on scenario construction for dynamically tackling the severity ranking problem of railway accidents. Firstly, the scenario is introduced into the selection of grading indicators of railway accidents, and a five-dimensional railway accident scenario expression model based on knowledge element is proposed to dynamically select and express the grading indicators. Secondly, an improved density peaks clustering algorithm based on k nearest neighbors and turning point (IDPC-KNN-TP) as the grading model of railway accidents is established, which optimizes the local density measurement, the selection of cluster center points, and the assignment strategy of density peaks clustering (DPC). Finally, the railway accidents from 2010 to 2021 in the UK as a case study are analyzed. The results show that the performance of IDPC-KNN-TP is better than others, and the grading algorithm in this paper has good practical performance. The dynamic grading strategy and the emergency disposal suggestions are put forward to provide a reference for the hierarchical response to railway accidents.

Adaptive density peak clustering algorithm combined with sparse search

With the advantages of few parameters and the ability to deal with clusters of arbitrary shape, the density peak clustering algorithm has attracted wide attention since it came out. However, the algorithm has problems such as high time complexity, poor clustering effect on complex data sets, and the need to manually select cluster centers. Aiming at the above shortcomings, an improved density peak clustering algorithm is proposed. Combined with the sparse search algorithm, the calculation of the similarity between each point and its nearest neighbor is simplified, and the problem of the high time complexity of the algorithm is overcome. A new local density definition method is adopted to make the density of data points better reflect the spatial structure of data distribution and to improve the clustering accuracy of the algorithm. Finally, a strategy for automatically selecting cluster centers is proposed to improve the adaptability of the algorithm. The algorithm is used to compare with the other improved algorithm on artificial data sets and real data sets. The experimental results show that the proposed algorithm can show a better clustering effect and can quickly and accurately identify various complex clusters.

Mobile Phone Data Feature Denoising for Expressway Traffic State Estimation

Due to their wide coverage, low acquisition cost and large data quantity, the mobile phone signaling data are suitable for fine-grained and large-scale estimation of traffic conditions. However, the relatively high level of data noise makes it difficult for the estimation to achieve sufficient accuracy. According to the characteristics of mobile phone data noise, this paper proposed an improved density peak clustering algorithm (DPCA) to filter data noise. In addition, on the basis of the long short-term memory model (LSTM), a traffic state estimation model based on mobile phone feature data was established with the use of denoising data to realize the estimation of the expressway traffic state with high precision, fine granules, and wide coverage. The Shanghai–Nanjing Expressway was used as a case study area for method and model verification, the results of which showed that the denoising method proposed in this paper can effectively filter data noise, reduce the impact of extreme noise data, significantly improve the estimation accuracy of the traffic state, and reflect the actual traffic situation in a fairly satisfactory manner.

Density Peaks Clustering Algorithm Based on a Divergence Distance and Tissue—Like P System

Density Peaks Clustering (DPC) has recently received much attention in many fields by reason of its simplicity and efficiency. Nevertheless, empirical studies have shown that DPC has some shortfalls: (i) similarity measurement based on Euclidean distance is prone to misclassification. When dealing with clusters of non-uniform density, it is very difficult to identify true clustering centers in the decision graph; (ii) the clustering centers need to be manually selected; (iii) the chain reaction; an incorrectly assigned point will affect the clustering outcome. To settle the above limitations, we propose an improved density peaks clustering algorithm based on a divergence distance and tissue—like P system (TP-DSDPC in short). In the proposed algorithm, a novel distance measure is introduced to accurately estimate the local density and relative distance of each point. Then, clustering centers are automatically selected by the score value. A tissue—like P system carries out the entire algorithm process. In terms of the three evaluation metrics, the improved algorithm outperforms the other comparison algorithms using multiple synthetic and real-world datasets.

An improved density peaks clustering algorithm based on natural neighbor with a merging strategy

Density peaks clustering (DPC) is a novel density-based clustering algorithm that identifies center points quickly through a decision graph and assigns corresponding labels to remaining non-center points. Although DPC can identify clusters with any shape, its clustering performance is still restricted by some aspects. Firstly, DPC works poorly on manifold datasets with different densities. Secondly, DPC is sensitive to the cutoff parameter dc. For the sake of addressing these issues and improving the performance of DPC, an improved density peaks clustering algorithm based on natural neighbor with a merging strategy (IDPC-NNMS) is proposed. IDPC-NNMS identifies a natural neighbor set of each data to obtain its local density adaptively, which can effectively eliminate the impact of the cutoff parameter on final results. Then, sub-clusters are formed after selecting as many center points as possible and allocating labels to remaining non-center points. These sub-clusters are merged by a novel merging strategy until the end conditions are satisfied. The performance of IDPC-NNMS is evaluated on both synthetic and real-world datasets, which fully proves the effectiveness and superiority of the proposed IDPC-NNMS algorithm.

ConDPC: Data Connectivity-Based Density Peak Clustering

As a relatively novel density-based clustering algorithm, Density peak clustering (DPC) has been widely studied in recent years. DPC sorts all points in descending order of local density and finds neighbors for each point in turn to assign all points to the appropriate clusters. The algorithm is simple and effective but has some limitations in applicable scenarios. If the density difference between clusters is large or the data distribution is in a nested structure, the clustering effect of this algorithm is poor. This study incorporates the idea of connectivity into the original algorithm and proposes an improved density peak clustering algorithm ConDPC. ConDPC modifies the strategy of obtaining clustering center points and assigning neighbors and improves the clustering accuracy of the original density peak clustering algorithm. In this study, clustering comparison experiments were conducted on synthetic data sets and real-world data sets. The compared algorithms include original DPC, DBSCAN, K-means and two improved algorithms over DPC. The comparison results prove the effectiveness of ConDPC.

An Improved Density Peak Clustering Algorithm for Multi-Density Data.

Density peak clustering is the latest classic density-based clustering algorithm, which can directly find the cluster center without iteration. The algorithm needs to determine a unique parameter, so the selection of parameters is particularly important. However, for multi-density data, when one parameter cannot satisfy all data, clustering often cannot achieve good results. Moreover, the subjective selection of cluster centers through decision diagrams is often not very convincing, and there are also certain errors. In view of the above problems, in order to achieve better clustering of multi-density data, this paper improves the density peak clustering algorithm. Aiming at the selection of parameter dc, the K-nearest neighbor idea is used to sort the neighbor distance of each data, draw a line graph of the K-nearest neighbor distance, and find the global bifurcation point to divide the data with different densities. Aiming at the selection of cluster centers, the local density and distance of each data point in each data division is found, a γ map is drawn, the average value of the γ height difference is calculated, and through two screenings the largest discontinuity point is found to automatically determine the cluster center and the number of cluster centers. The divided datasets are clustered by the DPC algorithm, and then the clustering results are perfected and integrated by using the cluster fusion rules. Finally, a variety of experiments are designed from various perspectives on various artificial simulated datasets and UCI real datasets, which demonstrate the superiority of the F-DPC algorithm in terms of clustering effect, clustering quality, and number of samples.

An improved density peak clustering algorithm guided by pseudo labels

Density peak clustering algorithms and their variants have achieved promising results in many fields over the last few years. However, most of these algorithms parameters requiring to be fine-tuned by users. When facing real-world data without ground-truths, it is often challenging and time-consuming to identify better parameter values for parametric clustering algorithms. Considering this, we propose a density peak clustering algorithm guided by pseudo labels (PLDPC), in which the manually pre-specified parameters are avoided through applying the mutual information criterion. Specifically, we first design a novel pseudo-label generation method based on the theory of co-occurrence. Then, we use the maximizing mutual information method to obtain better clustering results. To evaluate the effectiveness of the proposed PLDPC algorithm, we conduct extensive experiments on 23 datasets, including six synthetic and seventeen real-world datasets. The experimental results show that PLDPC outperforms three classical algorithms (i.e., K-means, DPC, and DBSCAN) and eight state-of-the-art (SOTA) clustering algorithms in most cases.

A Clustering Algorithm for Tumor Gene Data Based on Improved DPC Algorithm

Cluster analysis is a principal approach to discover unknown tumor subtypes. Innovative and effective cluster analysis methods are of great significance for tumor diagnosis and malignant tumor treatment. Existing studies on the cluster analysis of tumor gene data generally have defects in aspects such as unsatisfactory performance in clustering high-dimensional and high-noise data, and insufficient accuracy in selecting cluster centers. To overcome these defects, this paper performed cluster analysis on tumor gene data based on an improved Density peaks clustering (DPC) algorithm. At first, this paper elaborated on the composition and storage format of tumor tissue samples used in the experiment, gave the tumor gene expression profile data in the matrix format, and introduced the preprocessing process of gene expression profile data. Then, this paper carried out feature selection of tumor gene expression profile data. At last, this paper innovatively divided the target gene density into two parts of K-nearest neighbor local density and neighborhood density, thereby completing the improvement of conventional DPC algorithm and expanding its application scenarios. Combining with experiment, the clustering results of the algorithm before and after introducing the idea of Approximate Nearest Neighbor (ANN) were given, which had verified the effectiveness of the algorithm proposed in this paper.

Multimode process monitoring based on hierarchical mode identification and stacked denoising autoencoder

In modern plants, industrial processes generally operate under different modes, and reliable monitoring for such processes is highly important. One of the key challenges is how to accurately identify the various modes including steady modes and transitions modes. In this paper, a novel monitoring scheme based on hierarchical mode identification strategy and stacked denoising autoencoder (HMI-SDAE) is proposed for multimode processes. First, a novel mode division strategy called HMI is presented. In HMI, the Gaussian mixture model (GMM) is adopted to realize the preliminary identification of various modes by extracting the global distribution features of the variables. In this way, the whole multimode process is divided into multiple steady modes. An improved density peaks clustering algorithm based on local density relation search (LDRSDPC) is proposed to achieve the transition mode identification by fully utilizing the local distribution features of the process variables involved in any two adjacent steady modes and transition mode between them. A decision criterion combined with local density relation is constructed to automatically determine the clustering center. In this hierarchical way, multiple steady modes and transition modes are divided automatically and accurately. Secondly, the deep nonlinear features embedded in process variables are mined by SDAE, and the robust monitoring model is established for each steady mode. A monitoring statistic is constructed using the reconstruction error for detecting faults. The effectiveness and feasibility of the proposed HMI-SDAE monitoring scheme are illustrated with a numerical example and Tennessee Eastman (TE) process.

An improved density peaks clustering algorithm based on grid screening and mutual neighborhood degree for network anomaly detection

With the rapid development of network technologies and the increasing amount of network abnormal traffic, network anomaly detection presents challenges. Existing supervised methods cannot detect unknown attack, and unsupervised methods have low anomaly detection accuracy. Here, we propose a clustering-based network anomaly detection model, and then a novel density peaks clustering algorithm DPC-GS-MND based on grid screening and mutual neighborhood degree for network anomaly detection. The DPC-GS-MND algorithm utilizes grid screening to effectively reduce the computational complexity, improves the clustering accuracy through mutual neighborhood degree, and also defines a cluster center decision value for automatically selecting cluster centers. We implement complete experiments on two real-world datasets KDDCup99 and CIC-IDS-2017, and the experimental results demonstrated that the proposed DPC-GS-MND can detect network anomaly traffic with higher accuracy and efficiency. Together, it has a good application prospect in the network anomaly detection system in complex network environments.

Density Peaks Clustering Based on Feature Reduction and Quasi-Monte Carlo

Density peaks clustering (DPC) is a well-known density-based clustering algorithm that can deal with nonspherical clusters well. However, DPC has high computational complexity and space complexity in calculating local density ρ and distance δ , which makes it suitable only for small-scale data sets. In addition, for clustering high-dimensional data, the performance of DPC still needs to be improved. High-dimensional data not only make the data distribution more complex but also lead to more computational overheads. To address the above issues, we propose an improved density peaks clustering algorithm, which combines feature reduction and data sampling strategy. Specifically, features of the high-dimensional data are automatically extracted by principal component analysis (PCA), auto-encoder (AE), and t-distributed stochastic neighbor embedding (t-SNE). Next, in order to reduce the computational overhead, we propose a novel data sampling method for the low-dimensional feature data. Firstly, the data distribution in the low-dimensional feature space is estimated by the Quasi-Monte Carlo (QMC) sequence with low-discrepancy characteristics. Then, the representative QMC points are selected according to their cell densities. Next, the selected QMC points are used to calculate ρ and δ instead of the original data points. In general, the number of the selected QMC points is much smaller than that of the initial data set. Finally, a two-stage classification strategy based on the QMC points clustering results is proposed to classify the original data set. Compared with current works, our proposed algorithm can reduce the computational complexity from O n 2 to O N n , where N denotes the number of selected QMC points and n is the size of original data set, typically N ≪ n . Experimental results demonstrate that the proposed algorithm can effectively reduce the computational overhead and improve the model performance.

Improved Density Peaking Algorithm for Community Detection Based on Graph Representation Learning

There is a large amount of information in the network data that we can exploit. It is difficult for classical community detection algorithms to handle network data with sparse topology. Representation learning of network data is usually paired with clustering algorithms to solve the community detection problem. Meanwhile, there is always an unpredictable distribution of class clusters output by graph representation learning. Therefore, we propose an improved density peak clustering algorithm (ILDPC) for the community detection problem, which improves the local density mechanism in the original algorithm and can better accommodate class clusters of different shapes. And we study the community detection in network data. The algorithm is paired with the benchmark model Graph sample and aggregate (GraphSAGE) to show the adaptability of ILDPC for community detection. The plotted decision diagram shows that the ILDPC algorithm is more discriminative in selecting density peak points compared to the original algorithm. Finally, the performance of K-means and other clustering algorithms on this benchmark model is compared, and the algorithm is proved to be more suitable for community detection in sparse networks with the benchmark model on the evaluation criterion F1-score. The sensitivity of the parameters of the ILDPC algorithm to the low-dimensional vector set output by the benchmark model GraphSAGE is also analyzed.

An improved density peaks clustering algorithm by automatic determination of cluster centres

The fast search and find of density peaks clustering (FDP) is an algorithm that can gain satisfactory clustering results with manual selection of the cluster centres. However, this manual selection is difficult for larger and more complex datasets, and it is easy to split a cluster into multiple subclusters. We propose an automatic determination of cluster centres algorithm (A-FDP). On the one hand, a new decision threshold is designed in A-FDP combined with the InterQuartile Range and standard deviation. We select the points larger than the decision threshold as the cluster centres. On the other hand, these cluster centres are made as nodes to construct the connected graphs. These subclusters are merged by finding the connected components of the connected graph. The results show that the A-FDP can obtain better clustering results and have higher accuracy than other classical clustering algorithms on synthetic and UCI datasets.

On a two-stage progressive clustering algorithm with graph-augmented density peak clustering

Due to the rapidly growing volume and velocity of big data, real-time streaming data analysis has become increasingly important in many applications. To discover knowledge from such data, a wide range of machine learning techniques have been proposed and used in practice. Among them, clustering, which aims at grouping objects into different classes on the basis of their similarity, is the most common form of unsupervised learning. However, most existing clustering algorithms are designed for static data, and hence are not best suited for streaming data. In this paper, we propose PC-DPC, a two-stage progressive clustering algorithm with graph-augmented density peak clustering. PC-DPC first identifies clusters of streaming data using an improved density peak clustering algorithm, and then merges newly arriving data into the existing data pool by measuring inter-cluster structural similarity, which considers the distance between a center and representative points. We illustrate the superiority of PC-DPC over several state-of-the-art clustering algorithms in terms of clustering accuracy and running time on publicly available benchmark datasets.

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.