###### Abstract  
To discover the spatial-temporal patterns of sea surface temperature (SST) in the South China Sea (SCS), this paper proposes a spatial-temporal co-clustering algorithm optimized by information divergence. This method allows for the clustering of SST data simultaneously across temporal and spatial dimensions and is adaptable to large volumes of data and anomalous data situations. First, the SST data are initially clustered using the co-clustering algorithm. Second, we use information divergence as the loss function to refine the clustering results iteratively. During the iterative optimization of spatial clustering results, we treat the temporal dimension as a constraint; similarly, during the iterative optimization of temporal clustering, we treat the spatial dimension as a constraint. This is to ensure better robustness of the algorithm. Finally, this paper conducts experiments in the SCS to verify our algorithm. According to the analysis of the experimental results, we have drawn the following conclusions. First, the use of the spatial-temporal co-clustering algorithm reveals that the SST in the SCS exhibits strong seasonal patterns in the temporal clustering results. The spatial distribution of SST varies significantly in different seasons. There is a slight difference in SST between the northern and southern regions of the SCS in winter, but the largest difference is in summer. Second, during ocean anomalies, our proposed algorithm can identify the corresponding abnormal patterns. When ENSO occurs, the seasonal distribution pattern of SST in the SCS is destroyed and replaced by an abnormal temporal pattern. The results indicate that during ENSO events, the SST in specific months in the SCS exhibits a correlation with the SST observed 4-5 months afterward. spatial-temporal co-clustering; spatiotemporal patterns; ENSO; SCS; SST +
Footnote †: journal: MedicalSCS can provide a reference for predicting natural disasters in the SCS region and neighboring countries [6]. The spatial-temporal pattern mentioned here refers to the interdependent pattern of time and space, rather than a separate temporal or spatial pattern. SST data are typical spatial-temporal data, as SST shows strong continuity characteristics in space and time [7]. In terms of geographical space, there are usually similarities in the SST in adjacent areas due to ocean heat diffusion and ocean flow [8]. In terms of temporal characteristics, it usually reflects seasonality. Variations in SST are usually accompanied by complex nonlinear processes, including seasonal changes, interannual changes, and abnormal varieties caused by natural phenomena such as the ENSO [9]. Therefore, this paper combines co-clustering with information divergence to propose a novel spatial-temporal co-clustering algorithm that can be used to analyze spatial-temporal data. Information divergence is a way of quantifying the difference between two matrices. It can help to measure the information lost when using one matrix to approximate another matrix. The advantage of using information divergence as a loss function compared to other distance measures (such as Euclidean distance and Manhattan distance) is that it pays more attention to the data distributions, while distance loss functions often only focus on the distance values between data. For spatiotemporal data such as SST, using information divergence as the loss function of the spatial-temporal co-clustering algorithm can better capture the spatiotemporal distribution characteristics of SST data. The spatial-temporal co-clustering algorithm can not only discover the seasonal characteristics of SST, but also the abnormal time patterns of SST when ENSO events occur. It can also discover different spatial patterns in different temporal clusters. We experimented with our method on the SST dataset of the SCS. First, we selected SST data from 2003.12-2004.11 for experimentation to obtain the spatial-temporal patterns of the SST in the SCS.