Density peak clustering with attribute-level similarity and two-stage allocation

Density peak clustering (DPC) is a density-based clustering method that has attracted much attention in the academic community. DPC works by first searching density peaks in the dataset, and then assigning each data point to the same cluster as its nearest higher-density point. One problem with DPC is the determination of the density peaks, where poor selection of the density peaks could yield poor clustering results. Another problem with DPC is its cluster assignment strategy, which often makes incorrect cluster assignments for data points that are far from their nearest higher-density points. This study modifies DPC and proposes a new clustering algorithm to resolve the above problems. The proposed algorithm uses the radius of the neighborhood to automatically select a set of the likely density peaks, which are far from their nearest higher-density points. Using the potential density peaks as the density peaks, it then applies DPC to yield the preliminary clustering results. Finally, it uses single-linkage clustering on the preliminary clustering results to reduce the number of clusters, if necessary. The proposed algorithm avoids the cluster assignment problem in DPC because the cluster assignments for the potential density peaks are based on single-linkage clustering, not based on DPC. Our performance study shows that the proposed algorithm outperforms DPC for datasets with irregularly shaped clusters.

DPC-FSC: An approach of fuzzy semantic cells to density peaks clustering

Density Peaks Clustering (DPC) algorithm identifies cluster centers based on local density and relative distance, disregarding the effect of the sample's environment on its density. This makes it challenging to identify cluster centers in low-density regions. Moreover, the single-step allocation strategy of DPC algorithm lacks fault tolerance. If a sample point is incorrectly allocated, it can trigger a cascade of subsequent allocation error. To solve the aforementioned issue, a density peak clustering algorithm based on natural neighbors and diffusion allocation (NNDA-DPC) is proposed. Firstly, the concept of natural neighbors is introduced, and the local density of sample points is redefined by considering the density of sample points and the environment in which the sample points are located. This is done to reduce the influence of the sparsity of class clusters on the selection of class cluster centers. The clustering centers are automatically determined by computing the decision value. Secondly, the natural neighbor points of the selected clustering centers are assigned to the corresponding clustering centers to form the initial microclusters. Finally, the initial microclusters are formed based on the remaining sample points and the initial clusters. The final clustering result is obtained by assigning the sample points based on the correlation between the remaining sample points and the initial clusters, which helps prevent the cascading effect of assignment errors. We compared the NNDA-DPC algorithm with DPC and its enhanced versions on artificial and UCI datasets. The experimental results demonstrate that the NNDA-DPC algorithm can efficiently cluster the datasets.

A method of two-stage clustering learning based on improved DBSCAN and density peak algorithm

Density Peaks Clustering (DPC) is a density-based clustering algorithm that has the advantage of not requiring clustering parameters and detecting non-spherical clusters. The density peaks algorithm obtains the actual cluster center by inputting the cutoff distance and manually selecting the cluster center. Thus, the clustering center point is not selected on the basis of considering the whole data set. This paper proposes a method called G-KNN-DPC to calculate the cutoff distance based on the Gini coefficient and K-nearest neighbor. G-KNN-DPC first finds the optimal cutoff distance with Gini coefficient, and then the center point with the K-nearest neighbor. The automatic clustering center method can not only avoid the error that a cluster detects two center points but also effectively solve the traditional DPC algorithm defect that cannot handle complex data sets. Compared with DPC, Fuzzy C-Means, K-means, KDPC and DBSCAN, the proposed algorithm creates better clusters on different data sets.

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

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.

BackgroundSoma localization is an important step in computational neuroscience to map neuronal circuits. However, locating somas from large-scale and complicated datasets is challenging. The challenges primarily originate from the dense distribution of somas, the diversity of soma sizes and the inhomogeneity of image contrast.ResultsWe proposed a novel localization method based on density-peak clustering. In this method, we introduced two quantities (the local density ρ of each voxel and its minimum distance δ from voxels of higher density) to describe the soma imaging signal, and developed an automatic algorithm to identify the soma positions from the feature space (ρ, δ). Compared with other methods focused on high local density, our method allowed the soma center to be characterized by high local density and large minimum distance. The simulation results indicated that our method had a strong ability to locate the densely positioned somas and strong robustness of the key parameter for the localization. From the analysis of the experimental datasets, we demonstrated that our method was effective at locating somas from large-scale and complicated datasets, and was superior to current state-of-the-art methods for the localization of densely positioned somas.ConclusionsOur method effectively located somas from large-scale and complicated datasets. Furthermore, we demonstrated the strong robustness of the key parameter for the localization and its effectiveness at a low signal-to-noise ratio (SNR) level. Thus, the method provides an effective tool for the neuroscience community to quantify the spatial distribution of neurons and the morphologies of somas.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1252-x) contains supplementary material, which is available to authorized users.

The density peaks clustering (DPC) algorithm can identify clusters with various shapes and densities in the underlying dataset. However, the DPC algorithm cannot exactly find the true quantity of clustering centers when computing the local density, and it is difficult to handle non-convex datasets. Moreover, the DPC algorithm is difficult to identify boundary points and outliers without a reasonable allocation strategy when dealing with low-density points. To solve these limitations, a novel deviation density peaks clustering (DeDPC) algorithm is proposed. First, the local deviation of the spatial distance of datasets with different structures is utilised to replace the local density to generate a more reasonable clustering center decision graph. Second, a threshold is defined to further divide and process low-density points. Finally, outliers in low-density points can be accurately found to accurately cluster the dataset. To evaluate the performance of the DeDPC algorithm, experiments are conducted on synthetic and real-world datasets and the DeDPC is compared with other clustering methods. The DeDPC is also applied to medical image segmentation to further demonstrate its capability for medical image processing. The simulation results show that the DeDPC method has good validity and utility for both non-convex datasets and medical image segmentation.

Clustering is one of the most important topics in data mining and machine learning. The density peaks clustering (DPC) algorithm is a well-known density-based clustering method that can efficiently and effectively deal with non-spherical clusters. However, the computational methods of the local density and the distance measure are simple and easily ignore the correlation and the similarity between samples, and the manual setting of parameters has a great influence on the clustering results; therefore, the clustering performance of DPC is poor on the high-dimensional datasets. To address these issues, this paper presents an adaptive DPC algorithm with Fisher linear discriminant for the clustering of complex datasets, called ADPC-FLD. First, the kernel density estimation function is introduced to calculate the local density of the sample points. Pearson correlation coefficient between samples as weight is employed to construct a weighted Euclidean distance function to measure the distance between samples. This considers both the spatial structure and the correlation of the samples. Then, a novel density estimation entropy is proposed, and based on the minimization of density estimation entropy, the density estimation parameters are adaptively selected according to the distribution characteristics of the data, which can efficiently eliminate the influence of manual setting. Third, an adaptive strategy of cluster center selection is designed to avoid the error caused by the noise data as the cluster centers and the uncertainty of manually selecting the cluster centers. Finally, Fisher linear discriminant algorithm is used to eliminate the irrelevant information and reduce the dimensionality of high-dimensional data, following on which an adaptive DPC method is implemented on six synthetic datasets, thirteen UCI datasets and seven gene expression datasets for comparing with other related algorithms. The experimental results on 26 datasets show that the proposed algorithm significantly outperforms several outstanding clustering approaches in terms of clustering accuracy and efficiency.

Fluid evaluation plays a vital role in reserve calculation and perforation location selection in shale oil exploration. Manual classification with fixed cutoffs and the blind source separation (BSS) method are the main approaches used for fluid typing in NMR T1–T2 maps. To overcome the subjectivity of the manual method and the dependence of BSS on a large dataset, an approach that integrates a clustering method, density peak clustering (DPC), and a spectral fitting technique, the Gaussian mixture model (GMM), is introduced in this paper to classify fluid components and evaluate oil saturation from T1–T2 maps. To select the number of fluid types automatically, traditional DPC is improved by defining a metric rnew based on local outlier degree, local density, relative distance, and threshold r*. The clustering accuracy of the r*−DPC method is 83.64%, which is much higher than the 52.73% accuracy of traditional DPC, and the r*–DPC method achieves better performance in fluid partitioning than other commonly used clustering algorithms. With the fluid centers information provided by r*–DPC, the GMM method is implemented to fit and extract the T1–T2 signatures of multiple fluids from T1–T2 maps. The DPC–GMM method was applied to core T1–T2 measurements and T1–T2 logging datasets, and the experimental results reveal that the average relative error of oil saturation is between 17.10% and 21.63%, which is nearly 15% lower than that of the BSS method. Furthermore, the DPC–GMM method requires less time and is easier to implement, which can make it an efficient and practical approach to fluid evaluation.

A novel density peaks clustering algorithm based on Hopkins statistic

Density peak clustering based on relative density relationship

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.

The outlier detection technique is widely used in the data analysis for the clustering of data. Many techniques have been applied in the outlier detection to increase the efficiency of the data analysis. The Local Projection based Outlier Detection (LPOD) method effectively identifies neighbouring values of data, but this has the drawback of random selection of the cluster centre that affects the overall clustering performance of the system. In this study, the Adaptive Clustering by Fast Search and Find of Density Peak (ACFSFDP) is proposed to select the clustering centre and density peak. This ACFSFDP method is implemented with the min-max algorithm to find the number of categories that measured the local density and distance information. The density and distance are used to select the cluster centre, but density is not calculated on the existing distance based clustering techniques. The ACFSFDP method calculates cluster centre based on the density and distance during the clustering process, whereas the existing techniques randomly select the data centre. The results indicated that the ACFSFDP method is provided effective outlier detection compared with existing Clustering by Fast Search and Find of Density Peak (CFSFDP) methods. The ACFSFDP is tested on two datasets Pen-digits and waveform datasets. The experiment results proved that Area Under Curve (AUC) of the ACFSFDP is 99.08% on the Pen-Digit dataset, while the existing distance classifier method k-Nearest Neighbour has achieved 68.7% of AUC.