# Sparse Data-Extended Fusion Method for Sea Surface Temperature Prediction on the East China Sea
## 3 Implementation of the Proposed Approach
### Calculation Method of Association Relationship Based on Deep Learning  
This part calculates the data association relationship between different grids of remote sensing data. Neural networks have the ability to mine and discover the relationship between data. By using neural network algorithms, we can train large amounts of data and build relationships between data. Therefore, it has certain advantages in the calculation of the data association relationship between different grids of large-area remote sensing. In this paper, we use deep learning classification algorithms to classify spatiotemporal series data, determine the degree of association between data points, and use neural networks to construct data relationships.  
Suppose the spatio-temporal series data is \(D=\left\{X^{1},X^{2},\ldots,X^{n}\right\}\), where \(X^{i}=\left\{x_{1}^{i},x_{2}^{i},\ldots,x_{n}^{i}\right\}\) is a piece of time series data, and define the category of each data sample of \(X^{i}\) as the \(i\)th type, and \(x_{j}^{i}\) is the \(i\)th data sample of the \(j\)th time series. By using the neural network algorithm for data training, \(f(\cdot)\) can be calculated. Through data prediction of different data, the prediction category of each data sample can be obtained. The category sequence for the time series \(X^{i}\) data prediction can be defined as \(C^{i}=\left\{c_{1},c_{2},\ldots,c_{n}\right\}\), for different times. Sequence data points can be calculated by calculating the degree of penetration of other categories to this category. Therefore, the calculation method of data association is as follows:  
\[r_{i}^{j}=\sum_{i=1}^{n}\left[c_{i}=c_{j}\right]/n \tag{1}\]  
where \(n\) is the number of samples of data point \(X^{i}\), and \(r_{i}^{j}\) represents the relationship between data point \(X^{j}\) and data point \(X^{i}\).  
The neural network used in this paper is the Gated Recurrent Unit (GRU) network. The GRU network mainly includes the reset gate as Equation (2) and the update gate as Equation (3). The update gate is used to control the extent to which the state information at the previous moment is brought into the current state. The larger the value of the update gate, the more state information from the previous moment is brought in. The reset gate is used to control the degree of ignoring the state information at the previous moment. A smaller reset gate will produce a higher degree of ignoring.  
\[r_{t}=\sigma(W_{r}\cdot\left[h_{t-1},x_{t}\right]) \tag{2}\]  
\[z_{t}=\sigma(W_{z}\cdot\left[h_{t-1},x_{t}\right]) \tag{3}\]  
\[\widetilde{h}_{t}=\tanh(W_{t-1}^{-}\cdot\left[r_{t}\ast h_{t-1},x_{t}\right]) \tag{4}\]  
\[h_{t}=(1-z_{t})\ast h_{t-1}+z_{t}\ast\widetilde{h}_{t} \tag{5}\]  
\[y_{t}=\sigma(W_{o}\cdot h_{t}) \tag{6}\]In the above formula, \(Z_{t}\) and \(r_{t}\) represent the update gate and reset gate respectively. In essence, it is the same as Long-Short Term Memory (LSTM). The output \(h_{t-1}\) of the previous moment \(t-1\) is combined with the input \(x_{t}\) of the current moment to calculate various attenuation coefficients. The slight difference is that the linear transformation does not use bias. Because the memory state is also \(h_{t-1}\), it is directly updated. The final output network result \(h_{t}\) is as shown in Equation (5). This result is also the memory state of the network. The output result at each step is \(y_{t}\) is as Formula (6).  
We use a two-layer GRU network plus a fully connected layer network structure for network training in this paper; the network structure is show in Figure 2 below.  
The output result of the first layer of GRUCell is used as the input of the second layer of GRUCell network, and the output of the last GRUCell is connected to the fully connected layer, and the classification probability of each point can be directly obtained. Among them, the two-layer GRU network can receive and process more data information, and the fully connected layer can map data hiding information to each data category.