Density Peaks Clustering based on Nature Nearest Neighbor and Multi-cluster Mergers

Clustering by fast search and find of Density Peaks (DPC) has the advantages of being simple, efficient, and capable of detecting arbitrary shapes, etc. However, there are still some shortcomings: 1) the cutoff distance is specified in advance, and the selection of local density formula will affect the final clustering effect; 2) after the cluster centers are found, the assignment strategy of the remaining points may produce “Domino effect”, that is, once a point is misallocated, more points may be misallocated subsequently. To overcome these shortcomings, we propose a density peaks clustering algorithm based on natural nearest neighbor and multi-cluster mergers. In this algorithm, a weighted local density calculation method is designed by the natural nearest neighbor, which avoids the selection of cutoff distance and the selection of the local density formula. This algorithm uses a new two-stage assignment strategy to assign the remaining points to the most suitable clusters, thus reducing assignment errors. The experiment was carried out on some artificial and real-world datasets. The experimental results show that the clustering effect of this algorithm is better than those other related algorithms.

Observations of PKKPab Diffraction Waves Well Beyond Cutoff Distance

The core mantle boundary (CMB) features the most dramatic contrast in the physical properties within the Earth and plays a fundamental role in the understanding of the dynamic evolution of the Earth’s interior. Seismic core phases such as PKKP sample large area of the lowermost mantle and the uppermost core, thus providing valuable information of the velocity structures on both sides of the CMB. Diffraction Waves Well Beyond Cutoff Distance (PKKPab) is one branch of the triplicated PKKP that can be observed beyond its ray theoretical cutoff distance as a result of diffraction along the CMB. The travel time and slowness of the diffracted PKKPab (denoted as PKKPabdiff) can be used to constrain the P-wave velocities at the lowermost mantle, thus have been investigated in numerous studies. Previous results (Rost and Garnero, 2006) suggest that most of the observations of the PKKPabdiff waves are in the epicentral distance range of 95°–105° (minor arc convention) (PKKPabdiff diffraction length less than 10°). However, high-frequency (∼1 Hz) synthetic seismograms show that the PKKPabdiff waveforms could be observable at distance down to 65°, which indicates that the PKKPabdiff signals could be detected at distances less than 95° in observations. To explore the distance ranges in which PKKPabdiff is observable, we collected global three-component broadband waveforms from 246 events with source depth deeper than 100 km and magnitude above M 6 from 2007 to 2017 available at the Incorporated Research Institutions for Seismology Data Management Center. We analyzed the slowness, polarization, and amplitude of the candidate PKKPabdiff signals, and found 95 events with clear PKKPabdiffsignals, with nearly 60% of the events show PKKPabdiff diffraction lengths greater than 10°, and the longest diffraction distance is beyond 20°. These newly identified PKKPabdiff waves would substantially augment the dataset of core phases for improvements of the CMB velocity models.

Significance Support Vector Regression for Image Denoising

As an extension of the support vector machine, support vector regression (SVR) plays a significant role in image denoising. However, due to ignoring the spatial distribution information of noisy pixels, the conventional SVR denoising model faces the bottleneck of overfitting in the case of serious noise interference, which leads to a degradation of the denoising effect. For this problem, this paper proposes a significance measurement framework for evaluating the sample significance with sample spatial density information. Based on the analysis of the penalty factor in SVR, significance SVR (SSVR) is presented by assigning the sample significance factor to each sample. The refined penalty factor enables SSVR to be less susceptible to outliers in the solution process. This overcomes the drawback that the SVR imposes the same penalty factor for all samples, which leads to the objective function paying too much attention to outliers, resulting in poorer regression results. As an example of the proposed framework applied in image denoising, a cutoff distance-based significance factor is instantiated to estimate the samples’ importance in SSVR. Experiments conducted on three image datasets showed that SSVR demonstrates excellent performance compared to the best-in-class image denoising techniques in terms of a commonly used denoising evaluation index and observed visual.

A novel density peaks clustering algorithm based on K nearest neighbors with adaptive merging strategy

Recently the density peaks clustering algorithm (DPC) has received a lot of attention from researchers. The DPC algorithm is able to find cluster centers and complete clustering tasks quickly. It is also suitable for different kinds of clustering tasks. However, deciding the cutoff distance $${d}_{c}$$ d c largely depends on human experience which greatly affects clustering results. In addition, the selection of cluster centers requires manual participation which affects the efficiency of the algorithm. In order to solve these problems, we propose a density peaks clustering algorithm based on K nearest neighbors with adaptive merging strategy (KNN-ADPC). A clusters merging strategy is proposed to automatically aggregate over-segmented clusters. Additionally, the K nearest neighbors are adopted to divide data points more reasonably. There is only one parameter in KNN-ADPC algorithm, and the clustering task can be conducted automatically without human involvement. The experiment results on artificial and real-world datasets prove higher accuracy of KNN-ADPC compared with DBSCAN, K-means++, DPC, and DPC-KNN.

A novel bidirectional clustering algorithm based on local density

With the widely application of cluster analysis, the number of clusters is gradually increasing, as is the difficulty in selecting the judgment indicators of cluster numbers. Also, small clusters are crucial to discovering the extreme characteristics of data samples, but current clustering algorithms focus mainly on analyzing large clusters. In this paper, a bidirectional clustering algorithm based on local density (BCALoD) is proposed. BCALoD establishes the connection between data points based on local density, can automatically determine the number of clusters, is more sensitive to small clusters, and can reduce the adjusted parameters to a minimum. On the basis of the robustness of cluster number to noise, a denoising method suitable for BCALoD is proposed. Different cutoff distance and cutoff density are assigned to each data cluster, which results in improved clustering performance. Clustering ability of BCALoD is verified by randomly generated datasets and city light satellite images.

A novel bidirectional clustering algorithm based on local density

With the widely application of cluster analysis, the number of clusters is gradually increasing, as is the difficulty in selecting the judgment indicators of cluster numbers. Also, small clusters are crucial to discovering the extreme characteristics of data samples, but current clustering algorithms focus mainly on analyzing large clusters. In this paper, a bidirectional clustering algorithm based on local density (BCALoD) is proposed. BCALoD establishes the connection between data points based on local density, can automatically determine the number of clusters, is more sensitive to small clusters, and can reduce the adjusted parameters to a minimum. On the basis of the robustness of cluster number to noise, a denoising method suitable for BCALoD is proposed. Different cutoff distance and cutoff density are assigned to each data cluster, which results in improved clustering performance. Clustering ability of BCALoD is verified by randomly generated datasets and city light satellite images.

Entropy based distance cutoff for protein internal contact networks

Protein structure networks (PSNs) have long been used to provide a coarse yet meaningful representation of protein structure, dynamics, and internal communication pathways. An important question is what criteria should be applied to construct the network so that to include relevant interresidue contacts while avoiding unnecessary connections. To address this issue we systematically considered varying residue distance cutoff length and the probability threshold for contact formation to construct PSNs based on atomistic molecular dynamics in order to assess the amount of mutual information within the resulting representations. We found that the minimum in mutual information is universally achieved at the cutoff length of 5 Å, irrespective of the applied contact formation probability threshold in all considered, distinct proteins. Assuming that the optimal PSNs should be characterised by the least amount of redundancy, which corresponds to the minimum in mutual information, this finding suggests an objective criterion for cutoff distance and supports the existing preference towards its customary selection around 5 Å length, typically based to date on heuristic criteria.

A Novel Density Peaks Clustering Algorithm Based on K Nearest Neighbors With Adaptive Merging Strategy

Recently the density peaks clustering algorithm (dubbed as DPC) attracts lots of attention. The DPC is able to quickly find cluster centers and complete clustering tasks. And the DPC is suitable for many clustering tasks. However, the cutoff distance 𝑑𝑑𝑐𝑐 is depends on human experience which will greatly affect the clustering results. In addition, the selection of cluster centers requires manual participation which will affect the clustering efficiency. In order to solve these problem, we propose a density peaks clustering algorithm based on K nearest neighbors with adaptive merging strategy (dubbed as KNN-ADPC). We propose a clusters merging strategy to automatically aggregate the over-segmented clusters. Additionally, the K nearest neighbors is adopted to divide points more reasonably. The KNN-ADPC only has one parameter and the clustering task can be conducted automatically without human involvement. The experiment results on artificial and real-world datasets prove the higher accuracy of KNN-ADPC compared with DBSCAN, K-means++, DPC and DPC-KNN.

Improved Density Peaks Clustering Based on Natural Neighbor Expanded Group

Density peaks clustering (DPC) is an advanced clustering technique due to its multiple advantages of efficiently determining cluster centers, fewer arguments, no iterations, no border noise, etc. However, it does suffer from the following defects: (1) difficult to determine a suitable value of its crucial cutoff distance parameter, (2) the local density metric is too simple to find out the proper center(s) of the sparse cluster(s), and (3) it is not robust that parts of prominent density peaks are remotely assigned. This paper proposes improved density peaks clustering based on natural neighbor expanded group (DPC-NNEG). The cores of the proposed algorithm contain two parts: (1) define natural neighbor expanded (NNE) and natural neighbor expanded group (NNEG) and (2) divide all NNEGs into a goal number of sets as the final clustering result, according to the closeness degree of NNEGs. At the same time, the paper provides the measurement of the closeness degree. We compared the state of the art with our proposal in public datasets, including several complex and real datasets. Experiments show the effectiveness and robustness of the proposed algorithm.

The anterior incisural width as a preoperative indicator for intradural space evaluation: An anatomical investigation

Background: The opticocarotid triangle (OCT) and the carotico-oculomotor triangle (COT) are two anatomical triangles used in accessing the interpeduncular region. Our objective is to evaluate if the anterior incisural width (AIW) is an indicator to predict the intraoperative exposure through both triangles. Methods: Twenty sides of 10 cadaveric heads were dissected and analyzed. The heads were divided into the following: Group A – narrow anterior incisura and Group B – wide anterior incisura – using 26.6 mm as a cutoff distance of the AIW. Subsequently, the area of the COT and the OCT in the transsylvian approach was measured, along with the maximum widths through the two trajectories in modified superior transcavernous approach. Results: The COT in the wide group was shown to have a significantly larger area compared with the COT in the narrow group (38.4 ± 12.64 vs. 58.3 ± 15.72 mm, P < 0.01). No difference between the two groups was reported in terms of the area of the OCT (50.9 ± 19.22 mm vs. 63.5 ± 15.53 mm, P = 0.20), the maximum width of the OCT (6.6 ± 1.89 vs. 6.5 ± 1.38 mm, P = 1.00), or the maximum width of the COT (11.7 ± 2.06 vs. 12.2 ± 2.32 mm, P = 0.50). Clinical cases were included. Conclusion: An AIW <26.6 mm is an unfavorable factor related to a limited COT area in a transsylvian approach for pathologies at the interpeduncular fossa. Preoperative identification and measurement of a narrow AIW can suggest the need to add a transcavernous approach.