With the rapid development of computer technology, big data applications have permeated every aspect of life [1]. At the same time, the scale of data is also continuously growing, and the requirements for the computational speed of clustering algorithms are constantly increasing [2], [3], [4]. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm. Its main principle is to assess the closeness of sample points after determining the minimum number of samples and radius [5], [6]. The DBSCAN algorithm can effectively detect outliers in samples [7], [8]. However, since the DBSCAN algorithm requires operations on the entire dataset,it is generally necessary to establish the corresponding R* tree and plot the corresponding K-dist graph before clustering. These two steps consume significant computational resources [9], [10], [11]. In scenarios where computational resources are limited and the size of the dataset is substantial, the computational efficiency of the DBSCAN algorithm can be significantly affected. Implementing parallelization of the core object determination step in the DBSCAN algorithm can substantially improve the algorithm’s efficiency [12], [13], [14]. Therefore, ternary optical computers can be employed for parallel computation in subsequent calculations.

Prof. Yi Jin proposed the concept of ternary optical computers in 2003. In this novel optical computing system, two orthogonal polarization states and the absence of light are used to represent ternary information [15], [16]. Ternary optical computers offer the advantages of handling a vast number of data bits, parallel processing of multiple data [17], [18], and the allocation of processors on demand. After long-term development, the theory and application of TOC have made significant progress [19], [20]. Currently, a unique system has been formed in the areas of MSD adder and its related theories, division operator theory, TOC high-level language programming theory, and applications in high-performance computing fields [21], [22]. Junyong Yan proposed the decrease-radix design principle in 2007, which established the design specifications for logical operators on TOC [23]. Jiabao Jiang designed and implemented the SJ-MSD adder in 2021. This adder achieves parallel computing through five logic transformations (S1,S2,J1,J2,J3), providing an alternative path for the design of adders in TOC. Currently, the computing speed of electronic computers is still increasing, but in the long term, as the scale of data continues to grow, it will be hard to meet the rising computational demands.

The DBSCAN algorithm requires iterative expansion from an initial point outward. The rate of this expansion affects the formation of sample clusters, which in turn influences the efficiency of the algorithm. This paper designs a TOC-based DBSCAN algorithm that can assess points within a sample’s neighborhood in parallel once a point is determined to be a core density object, thereby accelerating cluster expansion. Additionally, this paper demonstrates the feasibility of the TOC-based DBSCAN algorithm through experiments. Finally, by comparing the algorithm efficiency with traditional electronic computers, it is concluded that the TOC-based DBSCAN algorithm has faster computational efficiency and lower power consumption.