# A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
## 2 Ensemble EMD with LR Related Works
### LSTM Neural Network  
Recurrent neural networks (RNNs) are primarily engineered to tackle nonlinear, time-varying issues. Their internal connections facilitate both forward and backward data propagation. Incorporating feedback loops enables convenient residual or weight updates during the forward pass. This capability proves particularly advantageous for time-series forecasting, empowering the extraction of patterns from historical data to predict future values. The fundamental architecture of an RNN is illustrated in Figure 4, where the leftmost column depicts the overarching RNN structure, while the rightmost column provides a detailed expansion thereof.  
The RNN module, denoted as \(h\) in Figure 4, processes input data \(x_{t}\) and yields an output \(y_{t}\) at time \(t\). Unlike traditional neural networks, RNNs share the parameters \(W_{y_{t}}\)  
Figure 4: Fundamental architecture of RNN.  
\(W_{hh}\), and \(W_{hx}\) across each layer. This parameter sharing implies that every step within the RNN performs analogous operations, albeit on different input-output pairs \((x_{t},y_{t})\). Consequently, the parameter space to be learned in RNNs is significantly reduced. As RNNs expand, they manifest as multilayer neural networks. In contrast to traditional setups where each layer possesses distinct parameters, RNNs maintain uniformity across layers. For instance, the \(W_{hh}\) parameters between the \(h_{t-1}\) and \(h_{t}\) layers remain consistent, as do those between the \(h_{t}\) and \(h_{t+1}\) layers. Likewise, the \(W_{hx}\) parameters between \(x_{t}\) and \(h_{t}\) and between \(W_{yh}\) between \(h_{t}\) and \(y_{t}\) remain identical throughout.  
In the RNN, each step involves an output and input, but not every step's input and output are crucial. Take predicting mathematical expression values as an example: we only need the output after inputting the last expression symbol, rather than that for each symbol input. The hidden layer of the RNN is its essence, being adept at capturing both short- and long-term information within time-series data. However, RNNs are plagued by the issue of vanishing gradients during network training. This issue can lead to indefinite increases in the training time, and can ultimately cause network paralysis. Hence, a simple RNN is suboptimal for predicting time series with long-term dependencies.  
The LSTM neural network addresses the gradient vanishing issue encountered by simple RNNs when dealing with time series with long-term dependencies. It introduces output, input, and forget gates to the network model, which enhances its capabilities. These gates, illustrated in Figure 5, incorporate sigmoid activations, effectively combating gradient disappearance. The memory cell, a key innovation in LSTM, stores essential state information, enabling it to adeptly capture long-term dependencies. Each gate module typically employs an activation function to facilitate nonlinear transformations or information filtering. For instance, the forget gate \(f_{t}\) decides which neuron state information to discard, enhancing the network's adaptability.