An optimized cluster density matrix embedding theory

We propose an optimized cluster density matrix embedding theory(CDMET).It reduces the computational cost of CDMET with simpler bath states.And the result is as accurate as the original one.As a demonstration,we study the distant correlations of the Heisenberg J_(1)-J_(2)model on the square lattice.We find that the intermediate phase(0.43≤sssim J_(2)≤sssim 0.62)is divided into two parts.One part is a near-critical region(0.43≤J_(2)≤0.50).The other part is the plaquette valence bond solid(PVB)state(0.51≤J_(2)≤0.62).The spin correlations decay exponentially as a function of distance in the PVB.

A Study on Numerical Calculation Method of Small Cluster Density in Percolation Model

Percolation theory deals with the numbers and properties of the clusters formed in the different occupation probability. In this Paper, we study the calculation method of small clusters. We calcu-lated the small cluster density of 1, 2 and 3 in the percolation model with the exact method and the numerical method. The results of the two methods are very close, which can be verified by each other. We find that the cluster density of all three kinds of small clusters reaches the highest value when the occupation probability is between 0.1 and 0.2. It is very difficult to get the analytical formula for the exact method when the cluster area is relatively large (such as the area is more than 50), so we can get the density value of the cluster by numerical method. We find that the time required calculating the cluster density is proportional to the percolation area, which is indepen-dent of the cluster size and the occupation probability.

Density Clustering Algorithm Based on KD-Tree and Voting Rules

Traditional clustering algorithms often struggle to produce satisfactory results when dealing with datasets withuneven density. Additionally, they incur substantial computational costs when applied to high-dimensional datadue to calculating similarity matrices. To alleviate these issues, we employ the KD-Tree to partition the dataset andcompute the K-nearest neighbors (KNN) density for each point, thereby avoiding the computation of similaritymatrices. Moreover, we apply the rules of voting elections, treating each data point as a voter and casting a votefor the point with the highest density among its KNN. By utilizing the vote counts of each point, we develop thestrategy for classifying noise points and potential cluster centers, allowing the algorithm to identify clusters withuneven density and complex shapes. Additionally, we define the concept of “adhesive points” between two clustersto merge adjacent clusters that have similar densities. This process helps us identify the optimal number of clustersautomatically. Experimental results indicate that our algorithm not only improves the efficiency of clustering butalso increases its accuracy.

Adaptive Density-Based Spatial Clustering of Applications with Noise(ADBSCAN)for Clusters of Different Densities

Finding clusters based on density represents a significant class of clustering algorithms.These methods can discover clusters of various shapes and sizes.The most studied algorithm in this class is theDensity-Based Spatial Clustering of Applications with Noise(DBSCAN).It identifies clusters by grouping the densely connected objects into one group and discarding the noise objects.It requires two input parameters:epsilon(fixed neighborhood radius)and MinPts(the lowest number of objects in epsilon).However,it can’t handle clusters of various densities since it uses a global value for epsilon.This article proposes an adaptation of the DBSCAN method so it can discover clusters of varied densities besides reducing the required number of input parameters to only one.Only user input in the proposed method is the MinPts.Epsilon on the other hand,is computed automatically based on statistical information of the dataset.The proposed method finds the core distance for each object in the dataset,takes the average of these distances as the first value of epsilon,and finds the clusters satisfying this density level.The remaining unclustered objects will be clustered using a new value of epsilon that equals the average core distances of unclustered objects.This process continues until all objects have been clustered or the remaining unclustered objects are less than 0.006 of the dataset’s size.The proposed method requires MinPts only as an input parameter because epsilon is computed from data.Benchmark datasets were used to evaluate the effectiveness of the proposed method that produced promising results.Practical experiments demonstrate that the outstanding ability of the proposed method to detect clusters of different densities even if there is no separation between them.The accuracy of the method ranges from 92%to 100%for the experimented datasets.

Encephalitis Detection from EEG Fuzzy Density-Based Clustering Model with Multiple Centroid

Encephalitis is a brain inflammation disease.Encephalitis can yield to seizures,motor disability,or some loss of vision or hearing.Sometimes,encepha-litis can be a life-threatening and proper diagnosis in an early stage is very crucial.Therefore,in this paper,we are proposing a deep learning model for computerized detection of Encephalitis from the electroencephalogram data(EEG).Also,we propose a Density-Based Clustering model to classify the distinctive waves of Encephalitis.Customary clustering models usually employ a computed single centroid virtual point to define the cluster configuration,but this single point does not contain adequate information.To precisely extract accurate inner structural data,a multiple centroids approach is employed and defined in this paper,which defines the cluster configuration by allocating weights to each state in the cluster.The multiple EEG view fuzzy learning approach incorporates data from every sin-gle view to enhance the model's clustering performance.Also a fuzzy Density-Based Clustering model with multiple centroids(FDBC)is presented.This model employs multiple real state centroids to define clusters using Partitioning Around Centroids algorithm.The Experimental results validate the medical importance of the proposed clustering model.

A novel fast classification filtering algorithm for LiDAR point clouds based on small grid density clustering

Clustering filtering is usually a practical method for light detection and ranging(LiDAR)point clouds filtering according to their characteristic attributes.However,the amount of point cloud data is extremely large in practice,making it impossible to cluster point clouds data directly,and the filtering error is also too large.Moreover,many existing filtering algorithms have poor classification results in discontinuous terrain.This article proposes a new fast classification filtering algorithm based on density clustering,which can solve the problem of point clouds classification in discontinuous terrain.Based on the spatial density of LiDAR point clouds,also the features of the ground object point clouds and the terrain point clouds,the point clouds are clustered firstly by their elevations,and then the plane point clouds are selected.Thus the number of samples and feature dimensions of data are reduced.Using the DBSCAN clustering filtering method,the original point clouds are finally divided into noise point clouds,ground object point clouds,and terrain point clouds.The experiment uses 15 sets of data samples provided by the International Society for Photogrammetry and Remote Sensing(ISPRS),and the results of the proposed algorithm are compared with the other eight classical filtering algorithms.Quantitative and qualitative analysis shows that the proposed algorithm has good applicability in urban areas and rural areas,and is significantly better than other classic filtering algorithms in discontinuous terrain,with a total error of about 10%.The results show that the proposed method is feasible and can be used in different terrains.

Intrusion Detection Algorithm Based on Density,Cluster Centers,and Nearest Neighbors

Intrusion detection aims to detect intrusion behavior and serves as a complement to firewalls.It can detect attack types of malicious network communications and computer usage that cannot be detected by idiomatic firewalls.Many intrusion detection methods are processed through machine learning.Previous literature has shown that the performance of an intrusion detection method based on hybrid learning or integration approach is superior to that of single learning technology.However,almost no studies focus on how additional representative and concise features can be extracted to process effective intrusion detection among massive and complicated data.In this paper,a new hybrid learning method is proposed on the basis of features such as density,cluster centers,and nearest neighbors(DCNN).In this algorithm,data is represented by the local density of each sample point and the sum of distances from each sample point to cluster centers and to its nearest neighbor.k-NN classifier is adopted to classify the new feature vectors.Our experiment shows that DCNN,which combines K-means,clustering-based density,and k-NN classifier,is effective in intrusion detection.

Density peaks clustering based integrate framework for multi-document summarization

We present a novel unsupervised integrated score framework to generate generic extractive multi- document summaries by ranking sentences based on dynamic programming （DP） strategy. Considering that cluster-based methods proposed by other researchers tend to ignore informativeness of words when they generate summaries, our proposed framework takes relevance, diversity, informativeness and length constraint of sentences into consideration comprehensively. We apply Density Peaks Clustering （DPC） to get relevance scores and diversity scores of sentences simultaneously. Our framework produces the best performance on DUC2004, 0.396 of ROUGE-1 score, 0.094 of ROUGE-2 score and 0.143 of ROUGE-SU4 which outperforms a series of popular baselines, such as DUC Best, FGB [7], and BSTM [10].

A Density Functional Study of N-Doped TiO_2 Anatase Cluster

A systematic study on geometry, electronic structure and vibrational properties of N-doped TiO2 anatase cluster, within the framework of the density functional theory, has been performed in this work. The calculations confirmed that the most structures in substitutional model consist of a two-coordinate bridge structure and a three-coordinate hollow structure. The calculated results can well explain the red shift in N-doped TiO2 observed in experiments. The study provides an illustration for the N-doped anatase from the viewpoint of chemical bonding theory.

Effect of Impurity on Critical Conditions of Colloidal Cluster Nucleation in Colloidal System

Due to depletion interactions, a few of colloidal spheres will be packed into cluster or clusters, even a phase transition may take place if the volume fraction of system is large enough. In a binary colloidal system, if the mole fraction of one component is very small, then it can be taken as the impurity of the other component. In this work, the effect of impurity on critical conditions of colloidal cluster nucleation was studied by Carnahan-Starling state equation and the principle of entropy maximum. The results show that, even the mole fraction of small-spheres is very small, the critical volume fraction is obvious smaller than that of one component system, so the influence on critical volume fraction from impurity is very huge and cannot be ignored. In addition, it is also found that, the larger the volume fraction of the system is, the larger cluster density can be packed, however, the critical size of nucleating cluster is almost independent of the density of the cluster.

Experimental and Theoretical Study of Hydrogen Atom Abstraction from C2H6 and C4H10 by Zirconium Oxide Clusters Anions

The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H- and Zr3O7H- are observed after the reaction. Den-sity functional theory calculations indicate that the hydrogen abstraction is favorable in the reaction of Zr2O5- with C2H6, which supports that the observed Zr2O5H- and Zr3O7H- are due to hydrogen atom abstraction from the alkane molecules. This work shows a newpossible pathway in the reaction of zirconium oxide cluster anions with alkane molecules.

Automatic velocity picking based on optimal key points tracking algorithm

Picking velocities from semblances manually is laborious and necessitates experience. Although various methods for automatic velocity picking have been developed, there remains a challenge in efficiently incorporating information from nearby gathers to ensure picked velocity aligns with seismic horizons while also improving picking accuracy. The conventional method of velocity picking from a semblance volume is computationally demanding, highlighting a need for a more efficient strategy. In this study, we introduce a novel method for automatic velocity picking based on multi-object tracking. This dynamic tracking process across different semblance panels can integrate information from nearby gathers effectively while maintaining computational efficiency. First, we employ accelerated density clustering on the velocity spectrum to discern cluster centers without the requirement for prior knowledge regarding the number of clusters. These cluster centers embody the maximum likelihood velocities of the main subsurface structures. Second, our proposed method tracks key points within the semblance volume. Kalman filter is adopted to adjust the tracking process, followed by interpolation on these tracked points to construct the final velocity model. Our synthetic data example demonstrates that our proposed algorithm can effectively rectify the picking errors of the clustering algorithm. We further compare the performances of the clustering method(CM), the proposed tracking method(TM), and the variational method(VM) on a field dataset from the Gulf of Mexico. The results attest that our method offers superior accuracy than CM, achieves comparable accuracy with VM, and benefits from a reduced computational cost.

A Health State Prediction Model Based on Belief Rule Base and LSTM for Complex Systems

In industrial production and engineering operations,the health state of complex systems is critical,and predicting it can ensure normal operation.Complex systems have many monitoring indicators,complex coupling structures,non-linear and time-varying characteristics,so it is a challenge to establish a reliable prediction model.The belief rule base(BRB)can fuse observed data and expert knowledge to establish a nonlinear relationship between input and output and has well modeling capabilities.Since each indicator of the complex system can reflect the health state to some extent,the BRB is built based on the causal relationship between system indicators and the health state to achieve the prediction.A health state prediction model based on BRB and long short term memory for complex systems is proposed in this paper.Firstly,the LSTMis introduced to predict the trend of the indicators in the system.Secondly,the Density Peak Clustering(DPC)algorithmis used todetermine referential values of indicators for BRB,which effectively offset the lack of expert knowledge.Then,the predicted values and expert knowledge are fused to construct BRB to predict the health state of the systems by inference.Finally,the effectiveness of the model is verified by a case study of a certain vehicle hydraulic pump.

Modeling of Energy Consumption and Effluent Quality Using Density Peaks-based Adaptive Fuzzy Neural Network

Modeling of energy consumption(EC) and effluent quality(EQ) are very essential problems that need to be solved for the multiobjective optimal control in the wastewater treatment process(WWTP). To address this issue, a density peaks-based adaptive fuzzy neural network(DP-AFNN) is proposed in this study. To obtain suitable fuzzy rules, a DP-based clustering method is applied to fit the cluster centers to process nonlinearity.The parameters of the extracted fuzzy rules are fine-tuned based on the improved Levenberg-Marquardt algorithm during the training process. Furthermore, the analysis of convergence is performed to guarantee the successful application of the DPAFNN. Finally, the proposed DP-AFNN is utilized to develop the models of EC and EQ in the WWTP. The experimental results show that the proposed DP-AFNN can achieve fast convergence speed and high prediction accuracy in comparison with some existing methods.

CLUSTERING OF DOA DATA IN RADAR PULSE BASED ON SOFM AND CDBW

Clustering is the main method of deinterleaving of radar pulse using multi-parameter.However,the problem in clustering of radar pulses lies in finding the right number of clusters.To solve this problem,a method is proposed based on Self-Organizing Feature Maps(SOFM) and Composed Density between and within clusters(CDbw).This method firstly extracts the feature of Direction Of Arrival(DOA) data by SOFM using the characteristic of DOA parameter,and then cluster of SOFM.Through computing the cluster validity index CDbw,the right number of clusters is found.The results of simulation show that the method is effective in sorting the data of DOA.

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.

Structure and magnetic properties of Osn （n=11～22） clusters

The structure and magnetic properties of Osn （n=11～22） clusters are systematically studied by using density functional theory （DFT）. For each size, the average binding energy per atom, the second-order differences of total energies and the highest occupied molecular orbital （HOMO）–the lowest unoccupied molecular orbital （LUMO） gaps are calculated to analyze the stability of the cluster. The structures of Os14 and Os18 clusters are based on a close-packed hexagonal structure, and they have maximum stabilities, so n=14, 18 are the magic numbers. The 5d electrons play a dominant role in the chemical reaction of Osn clusters. The magnetic moments of Osn clusters are quenched around n=12, and when n=18～22 the value approximates to zero, due to the difference of electron transfer.

A Novel Method of Deinterleaving Radar Pulse Sequences Based on a Modified DBSCAN Algorithm

A modified DBSCAN algorithm is presented for deinterleaving of radar pulses in modern EW environments.A main characteristic of the proposed method is that using only time of arrival of pulses,the method can sort the pulses efficiently.Other PDW information such as rise time,carrier frequency,pulse width,modulation on pulse,fall time and direction of arrival are not required.To identify the valid PRIs in a set of interleaved pulses,an innovative modification of the DBSCAN algorithm is introduced which is accurate and easy to implement.The proposed method determines valid PRIs more accurately and neglects the spurious ones more efficiently as compared to the classical histogram based algorithms such as SDIF.Furthermore,without specifying any input parameter,the proposed method can deinterleave radar pulses while up to 30%jitter is present in the associated PRI.The accuracy and efficiency of the proposed method are verified by computer simulations and real data results.Experimental simulations are based on different real and operational scenarios where the presence of missing and spurious pulses are also considered.So,the simulation results can be of practical significance.

几种经典聚类算法的比较研究

本文选取K-means、FCM、Spectral Cluster、Density Peak Cluster四种经典聚类算法作为研究对象,从理论和实验两个角度对它们进行比较研究。首先,本文介绍了聚类的含义、准则及应用;其次,本文分别阐述了四种算法的原理,并从理论角度分析它们的异同;再次,本文在UCI数据集上对四种算法执行了对比实验,比较它们的聚类准确率;最后,根据理论分析和对比实验的结果,得出四种算法适应不同类型数据集的结论。

A survey of density based clustering algorithms

Density based clustering algorithms(DBCLAs)rely on the notion of density to identify clusters of arbitrary shapes,sizes with varying densities.Existing surveys on DB-CLAs cover only a selected set of algorithms.These surveys fail to provide an extensive information about a variety of DBCLAs proposed till date including a taxonomy of the algorithms.In this paper we present a comprehensive survey of various DB-CLAS over last two decades along with their classification.We group the DBCLAs in each of the four categories:density definition,parameter sensitivity,execution mode and nature of*data and further divide them into various classes under each of these categories.In addition,we compare the DBCLAs through their common features and variations in citation and conceptual dependencies.We identify various application areas of DBCLAS in domains such as astronomy,earth sciences,molecular biology,geography,multimedia.Our survey also identifies probable future directions of DBCLAs where involvement of density based methods may lead to favorable results.