# Improved Particle Swarm Optimization for Sea Surface Temperature Prediction
## 1 Introduction  
Sea Surface Temperature (SST) is one of the crucial factors affecting the ocean climate. The occurrence of events such as El Nino, storm surges and red tides are closely related to SST. Therefore, in recent years, Sea Surface Temperature Prediction (SSTP) has attracted more and more attention in various marine-related fields such as marine meteorology, navigation, marine disaster prevention and mitigation, and marine fisheries. So far, researchers across the world have proposed many methods to predict SST, which can be divided into three categories: statistical forecasting [1], numerical forecasting [2], and empirical forecasting [3]. SST data are long-term data sequences and typically involve large data volumes. Many scholars regard SSTP as a time-series regression problem, and derive prediction models by fitting the curveof historical data [4]. However, SST data is well-known to suffer from high levels of redundant information, which makes it very difficult to realize accurate predictions through time-series regression, nor to capture the complex dynamics of SST trends. In 2013, [PERSON] et al., provided a prominent study showing how classic Support Vector Machine (SVM) could be used to predict SST in terms of raw data, slope and curvature [5]. Yet, they showed that SVM exhibited very similar performance when using raw data and curvature features, and was more effective than using slope. Better prediction accuracy was achieved with the more recent Long Short-Term Memory (LSTM) method [6]. This type of neural network has been widely used in diverse areas, thanks to its suitability for processing time series. In fact, [PERSON] et al. [7] were the first to use LSTM to predict SST. First, the SST sequence features were learned by LSTM layers. Then, a fully-connected layer was used to map the output of the LSTM layers to the final prediction result. Both SVM and LSTM tackle prediction accuracy. Yet, neither method is sufficiently efficient. Even more critically, marine operational forecasting requires significant improvements in SST trend predictions. Typically, empirical methods are used, of which the Analog Complexing (AC) algorithm [8] is a representative example. Nevertheless, AC has not shown sufficient accuracy in practical applications [9]. In this paper, our aim is to propose a new SSTP method, which not only can predict SST rapidly and accurately, but also can better model the SST trend. The main idea of our method is to use similarity measure to mine historical SSTs in order to extract sequences having similar trends, and then feed these into a suitable prediction method to infer future SSTs. When using this method to perform SSTP, we need to consider two important issues. First, time-series mining is critically sensitive to the accuracy of the similarity measure method; thus, any unexpected error in the mined data will dominate the prediction result. We solve this problem by a combination of similarity measure and multiple time-series regression. Another criticality is introduced by the choice the regression model parameters, which have a dramatic impact on the performance of the prediction model. We tackled this issue as a bi-objective optimization problem. In fact, our solution is dubbed DSL, since it is evolved from three building blocks: Dynamic Time Warping (DTW) [10], SVM [11], and Local-search enabled parameters optimization [12]. It consists of three parts:  
1. Using Dynamic Time Warping (DTW) to mine the similarities in historical SST series. DTW has been chosen as the result of an experimental, comparative analysis of three representative time-series SST similarity methods. It led to the highest prediction accuracy, it better modeled the SST trends, and was found to be suitable to mining SST long-term time series. 2. Training a Support Vector Machine (SVM) using the top-k similar patterns, deriving a robust SSTP model that offers a 5-day prediction window based on multiple SST input sequences.