###### Abstract
[28] introduced Principal Component Analysis (PCA) into the KNN-DPC model to perform dimensionality reduction operations on high-dimensional data before clustering. Although the above two algorithms have good feasibility and can obtain satisfactory results on relatively high-dimensional datasets, when the dataset presents vertical stripes, the clustering can be reduced to poor results. [PERSON] et al. [29] used PCA, autoencoder (AE), and t-distributed stochastic neighbor embedding (t-SNE) to automatically extract features from high-dimensional data and then used Quasi-Monte Carlo (QMC) to estimate the distribution of low-dimensional samples to obtain clustering results. [PERSON] et al. [30] first convert high-dimensional data into a two-dimensional space using t-SNE and cluster low-dimensional data using mutual nearest neighbors. The above two algorithms both use dimensionality reduction technology to process high-dimensional data, which can easily cause information loss. [PERSON] et al. [31] provided feasible channels for data of different dimensions to achieve dimensionality reduction of complex data. Aiming at the \"bad label\" delivery in the DPC, [PERSON] et al. [32] improved the validity of DPC by collecting information on the dynamics of nearest neighbors. [PERSON] et al. [33] put all data points into polar coordinates, calculated the distance and cosine values between any two points, and finally output the results with a sparse matrix. It can be efficient to minimize the running time of DPC. [PERSON] et al. [34] proposed a two-step clustering using shared nearest-neighbor information. [PERSON] et al. [35] redefined local density by taking into account information about nearest neighbors. [PERSON] et al. [36] grouped samples with k of the same nearest neighbors into a cluster. [PERSON] et al. [37] established a similarity fusion matrix to dynamically update the label information. All the above algorithms consider only the K nearest neighbors around the leftover points and lack consideration of global information. [PERSON] et al. [38] proposed the use of evidence theory to collect and fuse neighbor information of the leftover samples, which can effectively solve the error message delivery. However, it is difficult to solve the conflict problem, and the fusion accuracy is not enough. To surmount the above-mentioned defects, this paper put forward a novel density peaks clustering algorithm with isolation kernel and K-induction. The following are the major contributions:  
1. The isolation kernel is introduced and optimized. In this paper, the traditional distance is replaced by an optimized isolation kernel, which increases the similarity of two samples in a sparse domain and decreases the similarity of two samples in a dense domain. It solves the problem of poor applicability of high-dimensional data, further improves the accuracy of the algorithm, and solves the failure of traditional distance in high-dimensional spaces;
2. Three-way clustering is introduced, and the interval sets of the core domain and boundary domain are used to represent the clustering result. First, the KNN based on the optimized isolation kernel is exploited to find the \(K\) neighbors of the core domain center, and the initial core domain is obtained. Then, the range of the initial core domain is continuously expanded through the average similarity to obtain the final core domain;
3. The K-induction similarity is proposed. According to the K-induction similarity, each leftover point is allocated to the boundary domain of the cluster where the neighbor point with the largest K-induction similarity is located, which effectively avoids the domino effect and better solves the \"bad label\" delivery. The rest of the paper is as follows: The DPC, the isolation kernel, and the three-way clustering are detailed in Section 2. The IKDC is further elaborated upon in Section 3. The preliminary results are displayed in Section 4 to support the efficiency of the IKDC. The implications and future work are mentioned in Section 5.