###### Abstract  
Density peaks clustering (DPC) algorithm can process data of any shape and is simple and intuitive. However, the distance between any two high-dimensional points tends to be consistent, which makes it difficult to distinguish the density peaks and easily produces \"bad label\" delivery. To surmount the above-mentioned defects, this paper put forward a novel density peaks clustering algorithm with isolation kernel and K-induction (IKDC). The IKDC uses an optimized isolation kernel instead of the traditional distance. The optimized isolation kernel solves the problem of converging the distance between the high-dimensional samples by increasing the similarity of two samples in a sparse domain and decreasing the similarity of two samples in a dense domain. In addition, the IKDC introduces three-way clustering, uses core domains to represent dense regions of clusters, and uses boundary domains to represent sparse regions of clusters, where points in the boundary domains may belong to one or more clusters. At the same time as determining the core domains, the improved KNN and average similarity are proposed to assign as many as possible to the core domains. The K-induction is proposed to assign the leftover points to the boundary domain of the optimal cluster. To confirm the practicability and validity of IKDC, we test on 10 synthetic and 8 real datasets. The comparison with other algorithms showed that the IKDC was superior to other algorithms in multiple clustering indicators. DPC; high-dimensional data; three-way clustering; isolation kernel; K-induction +
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parameter and is not suitable for datasets with small differences in density. DBSCAN is only effective for spherical data and has a poor impact on aspheric data. [PERSON] et al. [26] proposed the hierarchical density-based spatial clustering of applications with noise (HDBSCAN). It combined DBSCAN with hierarchical clustering, redefined the distance between samples, and solved the problem that DBSCAN relies heavily on input parameters. However, this algorithm does not work well with boundary points. DPC was proposed by [PERSON] et al. [25]. It eliminates the drawbacks of DBSCAN and HDBSCAN, which are only valid for spherical data, can find density peak points with fewer parameters, and can efficiently assign points and remove noise. Meanwhile, DPC can automatically find the cluster centers and realize efficient clustering of data of any shape. However, there are still some drawbacks with DPC, mainly in two aspects: (1) poor applicability in high-dimensional spaces. With the advent of massive data, the dimensionality of the data is growing exponentially. When the dimensionality of data is high, it can be proven by the theorem of large numbers that the sum of independent random variables converges to a fixed value when the size of the variables is large, at which time the distances between high-dimensional samples tend to be equal. This means that the traditional distance formula becomes meaningless when calculating the distance between high-dimensional samples, which leads to a poor clustering effect; (2) error message delivery. The leftover points are directly allocated to the cluster in which the closest and denser point is located, without consideration of the information of the neighboring points. If a point is incorrectly assigned during this process, this error will be passed on to subsequent points, causing points that should not belong to a cluster to be assigned to a cluster, thus resulting in clustering failure; (3) deviation from human semantic interpretation. DPC belongs to hard clustering and does not take human semantic interpretation into account. Aiming at the poor practicability of DPC in high-dimensional data, [PERSON] et al. [27] introduced the grid granularity framework into DPC to address the poor clustering of DPC on large-scale datasets. [PERSON] et al.