Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks clustering algorithm with sparse search and K-d tree is developed to solve this problem. Firstly, a sparse distance matrix is calculated by using K-d tree to replace the original full rank distance matrix, so as to accelerate the calculation of local density. Secondly, a sparse search strategy is proposed to accelerate the computation of relative-separation with the intersection between the set of k nearest neighbors and the set consisting of the data points with larger local density for any data point. Furthermore, a second-order difference method for decision values is adopted to determine the cluster centers adaptively. Finally, experiments are carried out on datasets with different distribution characteristics, by comparing with other six state-of-the-art clustering algorithms. It is proved that the algorithm can effectively reduce the computational complexity of the original DPC from O(n 2 K) to O(n(n 1−1/K + k)). Especially for larger datasets, the efficiency is elevated more remarkably. Moreover, the clustering accuracy is also improved to a certain extent. Therefore, it can be concluded that the overall performance of the newly proposed algorithm is excellent.INDEX TERMS Density peaks clustering, sparse search strategy, K-d tree, computational complexity, second-order difference method.

When the density peak clustering algorithm deals with complex datasets and the problem of multiple density peaks in the same cluster, the subjectively selected cluster centers are not accurate enough, and the allocation of non-cluster centers is prone to joint and several errors. To solve the above problems, we propose a new density peak clustering algorithm based on cluster fusion strategy. First, the algorithm screens out the candidate cluster centers by setting two new thresholds to avoid the influence of noise points and outliers. Second, the remaining data points are allocated according to the density peak clustering algorithm to obtain the initial clusters. Third, considering the structural characteristics and spatial distribution of datasets, the new definitions of boundary points, inter-cluster intersection density and intercluster boundary density are provided. To correctly classify the clustering problems with multiple density peaks in the same cluster, a new cluster fusion strategy is proposed, which not only corrects the joint and several errors in the allocation of data points, but also correctly selects the cluster centers. Finally, to test the effectiveness of the proposed clustering algorithm, which is compared with DPC-KNN, DPC, K-means and DBSCAN on nine synthetic datasets and six real datasets. The experimental results demonstrate that the clustering performance of the proposed algorithm outperforms that of other algorithms.INDEX TERMS Clustering; density peaks; candidate cluster center; cluster fusion strategy;

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This paper obtained the mechanical properties of 1Cr18Ni9Ti by the static tensile test, got the corresponding relationship between the 1Cr18Ni9Ti coefficient of linear expansion, thermal conductivity and temperature changes, and simulated the process of 1Cr18Ni9Ti cutting with the finite element simulation software, then analysised the reason why the deviation of the finite element simulation results and measured data increased with the cutting speed improved. These studies provide some important references for the finite element simulation and revealing the tool wear and breakage mechanism.