# Density Peaks Clustering Algorithm Based on a Divergence Distance and Tissue--Like P System
## 1 Introduction
Despite the proliferation of new approaches, there are still several drawbacks that have an impact on clustering outcomes. Table 1 represents the main four properties of the various improvements of the density peaks clustering methods considering their evaluations. As a new research content of biological computing, membrane computing (also known as the P system) draws inspiration from the organism's own operating mechanisms and cooperation principles; that is, the structure of cells and tissues [30]. It is a model first proposed by [PERSON] [31] in 1998. In membrane computing, there are mainly three types: a cell-like P system [32], a tissue--like P system [33] and a neural-like P system [34]. Every living cell is a running reaction unit of the P system, and each unit independently works. That is to say, each unit of the P system is independently calculated in parallel. The P system's high level of parallelism means that it is frequently used with other algorithms to increase computing efficiency [35]. So far, the research content of the P system has primarily contained theoretical analysis [36] and application studies [37]. Numerous studies have also been conducted using clustering algorithms in conjunction with membrane computing [38]. In 2012, [PERSON] et al. [39] first combined membrane computing with clustering algorithms. In 2016, [PERSON] et al. [40] designed a new clustering algorithm by combining the PSO algorithm with the tissue--like P system. In 2020, [PERSON] et al. [23] introduced a density peaks clustering algorithm based on the K-nearest Shannon entropy and tissue--like P system. \begin{table}
\begin{tabular}{c} Non-iterative \\ Using a voting \\ \end{tabular} & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of various clustering algorithms. In 2021, [PERSON] et al. [41] proposed a spectral clustering method based on the coupling P system. It is possible to improve the performance of DPC in some cases using the variants mentioned above. Nevertheless, as mentioned earlier, DPC still has shortcomings, such as the use of Euclidean distance, the manual selection of clustering centers and the chain reaction. To address the above drawbacks, we propose an improved density peaks clustering algorithm based on divergence distance and a tissue--like P system, and verify the clustering performance in this paper. From the perspective of clustering, the TP-DSDPC can be viewed as a novel variant of DPC. From the perspective of membrane computing, the TP-DSDPC is a new variant of TP systems that can process clustering problems. The following are the main contributions of our work:  
* To eliminate the influence of Euclidean distance, a new distance metric--divergence distance--is proposed. * To redefine the formula for calculating local density and relative distance, and automatically select the clustering centers according to the score value. * The TP-DSDPC algorithm is integrated with a tissue--like P system, and optimizes the efficiency of the algorithm using P system's computational parallelism in theory. * The clustering performance of TP-DSDPC is simulated and verified on synthetic and UCI datasets. The remainder of this study is structured as follows. Section 2 introduces the fundamental principles and steps of the DPC algorithm and relevant notions of the P system. Section 3 presents the TP-DSDPC algorithm at length. The performance of TP-DSDPC through experimental results and the analysis of datasets is demonstrated in Section 4. Conclusions are outlined in Section 5, along with suggestions for future investigations.