## 3 Review of Methods
### Long Short-Term Memory (LSTM)  
In 1997, [PERSON] and [PERSON] [78] introduced LSTM cells, which have been investigated and enhanced in the works of [PERSON], [PERSON], and [PERSON] [79; 80; 81]. In contrast to RNNs, _Long Short-Term Memory_ networks are efficient in managing longer sequences and are able to reduce the problems that lead to the restricted use of simple RNNs. An LSTM cell contains short-term and long-term capabilities, which enable the memorization and recognition of the most significant inputs using three _gate controllers_ (see Figure 7). Figure 6: Stacked RNN: Generalized structure and temporal unrolled variant. Figure 7: Standard representation of a Peephole Long Short-Term Memory cell. The _input gate_ controls the fraction of the main layer output using the input that is used for the memory. For the Peephole Convolutional LSTM, a variation of the standard Peephole LSTM, to be suitable for processing images, it is calculated using the current input, \(x_{t}\), the previous short-time memory, \(h_{t-1}\), and the previous long-time memory, \(c_{t-1}\). These are multiplied with the corresponding weighting matrices, \(W_{x,i}\), \(W_{h,j}\), and \(W_{x,i}\), using matrix multiplication or element-wise multiplication (denoted as \(*\) and \(\circ\), respectively), and passed to a nonlinear function along with a bias term (see Equation (17)). In contrast to the input gate, the _forget gate_ defines the fraction of the long-term memory that has to be deleted. Similarly, the input and both memory inputs are multiplied with the matrices, \(W_{x,f}\), \(W_{h,f}\), and \(W_{x,f}\), respectively, and added to another bias term, prior to being passed to the same nonlinear activation function (see Equation (16)). This forms the basis for the updates of the memory states, where the current long-time memory (or cell state), \(c_{t}\), is calculated as the sum of the previous long-time memory, \(c_{t-1}\), weighted by the forget gate and the new candidate for the cell state, which is the tanh-activated linear combination of the weighted input and the previous short-time memory weighted by the input gate (see Equation (18)). Finally, the _output gate_ determines the part of the long-term memory that is used as the current output, \(y_{t}\), and the short-term memory for the next time step. For this, the current short-time memory of the LSTM cell is calculated by the tanh-activated current long-time memory, \(c_{t}\), weighted by the output gate, which itself is calculated using the current input, the previous short-time state, and the current long-time memory state (see Equations (19) and (20)). \[f_{t} =\sigma(x_{t}*W_{x,f}+h_{t-1}*W_{h,f}+c_{t-1}\circ W_{c,f}+b_{f}) \tag{16}\] \[i_{t} =\sigma(x_{t}*W_{x,i}+h_{t-1}*W_{h,i}+c_{t-1}\circ W_{c,i}+b_{1})\] (17) \[c_{t} =f_{t}\circ c_{t-1}+i_{t}\circ\tanh(x_{t}*W_{x,c}+h_{t-1}*W_{h,c}+ b_{c})\] (18) \[o_{t} =\sigma(x_{t}*W_{x,o}+h_{t-1}*W_{h,o}+c_{t}\circ W_{c,o}+b_{o})\] (19) \[h_{t} =o_{t}\circ\tanh(c_{t}) \tag{20}\]  
[PERSON] et al. [46] used a 77 GHz FMCW radar to collect data from nine subjects performing 12 different coarse- and fine-grained activities, namely events and gestures. Using sequential range-Doppler and micro-Doppler maps, five different neural networks, including an LSTM, a 1D CNN-LSTM, a 2D CNN, a 2D CNN-LSTM, and a 3D CNN, were investigated using 1505 and 2347 samples of events and gestures with regard to performance, modality, optimal sample length, and complexity. It was shown that the 3D CNN resulted in an accuracy of 87.78% for events and 97.03% for gestures. [PERSON] et al. [57] derived a method for through-the-wall classification and focused on the problem of unknown temporal allocation of activities during recognition, which can significantly impact accuracy.