## 2 Materials and Methods
### RNN Autoencoder-Based Method for Extracting Capability Features
#### 2.2.1 RNN Autoencoder Architecture Design  
(1) Method for supervised feature extraction  
A Recurrent Neural Network (RNN) is a neural network model dealing with time series, which enables the model to be trained and generalized to variable length time series samples by sharing parameters at different moments, and thus, it can dynamically extract features for contingency [21]. The encoder-decoder architecture is a variant of the RNN model. Data compression, feature extraction, and anomaly detection are just a few of the machine learning tasks that have been successfully completed using autoencoders, which are a class of neural networks. We provide a thorough overview of the architecture of autoencoders in this paper. The encoder and the decoder are the two main components that make up an autoencoder's architecture. The encoder is in charge of reducing the dimensions of the input data, and the decoder is in charge of reassembling the input data from the compressed  
Figure 1: Feature extraction idea. representation. The reconstruction error, also known as the difference between input data and output, is minimized by the architecture of an autoencoder. Typically, multi-layer perceptrons (MLPs), or fully connected neural networks, are used to implement the encoder and decoder. The encoder converts the input data into a compressed representation using one or more hidden layers. Hyperparameters like the number of hidden layers and the number of neurons in each layer are typically figured out through trial and error. The decoder, which is the exact opposite of the encoder, converts the compressed representation into a reconstructed output using one or more hidden layers. The decoder can reconstruct the input data with little loss of information because the number of hidden layers and neurons in each layer is typically the same as those in the encoder. The mean-squared error (MSE), which gauges the discrepancy between the input data and output, is frequently used as the loss function to train an autoencoder. Stochastic gradient descent (SGD) or one of its variants is typically the optimization algorithm used to minimize the loss function. Autoencoders are neural networks that can learn to compress and reconstruct data, to put it briefly. They consist of a decoder that reconstructs the input data from the compressed representation and an encoder that compresses the input data into a lower-dimensional representation. The loss function used to train the autoencoder is typically the mean-squared error, and the architecture of an autoencoder is typically implemented using fully connected neural networks. Figure 2 shows how it maps the input sequence to the output sequence. Figure 2: Encoder–decoder architecture. Assume that the input is a sequence of meteorological disaster response capability characteristics. \[x=\left(x^{(1)},x^{(2)},\cdots,x^{(T_{x})}\right) \tag{1}\]  
where \(T_{x}\) is the length of the sequence \(x\). If \(x^{(t)}\) is an M-dimensional feature vector, then  
\[x^{(t)}=\left(x_{1}^{(t)},x_{2}^{(t)},\ldots x_{M}^{(t)}\right) \tag{2}\]  
where \(x_{n}^{(t)}\) denotes the \(n\)th dimensional original capability characteristics of the weather disaster emergency subject to be evaluated at moment \(t\), and \(M\) is the dimension of the initial capability characteristics. The output of the model is a sequence of ability levels. \[y=\left(y^{(1)},y^{(2)},\cdots,y^{(T_{y})}\right) \tag{3}\]  
where \(T_{y}\) is the length of the sequence \(y\). The calculation method of intermediate state \(h^{(t)}\) is shown in Equation (4). \[h^{(t)}=g\left(W_{hh}h^{(t-1)}+W_{hh}x^{(t)}\right),\;t\in\{1,2,\ldots,T_{x}\} \tag{4}\]  
where \(g\) stands for activation function. \(W_{xh}\), \(W_{hy}\), and \(W_{hh}\) are the mapping matrices of input values to hidden states, hidden states to output values, and hidden states to hidden states, respectively. \(h^{(0)}\) is usually initialized as 0 vectors.