## 3 Review of Methods
### Convolutional Neural Networks  
Since their introduction in the 1980s by [PERSON], _Convolutional Neural Networks_ (_CNN_) have gained importance in science, especially in the signal-processing domain. As for other scientific fields, e.g., computer vision and speech recognition, the application of CNNs has been carried out for human activity recognition in numerous works in recent decades [40; 41; 48]. Convolutional Neural Networks are architectures that consist of stacked neural layers of certain functional types. The basis is formed by sequences of _convolutional layers_ and _pooling layers_. Convolutional layers are sets of convolutional filters that connect the neurons in the current layer to local sections (receptive fields) in the previous layer or input layer (see Figure 5). The filters apply a convolution based on the receptive field size, stride, and weights to the neurons of the previous layers. This process is called _feature extraction_, as it creates _feature maps_ using _activation functions_, e.g., ReLU, sigmoid, tanh, etc., that contain information about the most active neurons with regard to that specific filter. A two-dimensional discrete convolution is applied using the following general formula  
\[S[i,j]=(I*K)[i,j]=\sum_{m}\sum_{n}I[i+m,j+n]\cdot K[m,n] \tag{15}\]where \(K\) is the kernel with the indices \(m\) and \(n\), and \(I\) is the input or preceding layer with the indices \(i\) and \(j\). The determination of the filter weights is the main task in the learning process. In contrast to _fully connected networks_ (_FCNs_), this structure reduces the number of weights and, therefore, the computational effort, while preserving a certain degree of generalization. Pooling layers perform a subsampling task to reduce the amount of information and, therefore, the computational load and increase the degree of invariance to slight variations in the data of the previous layer. The most common pooling layer types are the _maximum pooling layer_ and the _average pooling layer_. The former selects the neuron with the highest value within its specific receptive field, whereas the latter takes the average value of all neurons of the receptive field of the previous layer. Finally, _fully connected layers_ connect the neurons containing the results of the convolutional process to the neurons of the _output layer_ for a classification task through flattening. The degree of generalization can be increased by inserting _dropout layers_, which reduce the number of neurons. [PERSON], [PERSON], and [PERSON] [53] applied a multiclass SVM, an AE, a CNN, and a CAE to classify 12 aided and unaided coarse-grained human activities. Using a 4.0 GHz CW radar system to create spectrograms, domain-specific features, e.g., cadence velocity diagrams (_cds_), as well as non-domain features, e.g., cepstral coefficients, LPC, and DCT, were derived. The sample sizes ranged from 50 (sitting) to 149 (wheelchair) for each class. The CAE-based approach achieved the highest accuracy of 94.2%, followed by the CNN (90.1%), AE (84.1%), and multiclass SVM (76.9%). [PERSON] et al. [48] used a time-distributed CNN enhanced with a Bidirectional LSTM to classify five human full-body activities consisting of boxing, jumping, jacks, jumping, squats, and walking, based on mmWave radar point clouds. The dataset was collected using a commercial off-the-shelf FMCW radar system in the 76-81 GHz frequency range capable of estimating the target direction. The dataset consisted of 12,097 samples for training, 3538 for testing, and 2419 for validation, where each sample consisted of a voxelized representation with dimensions of \(60\times 10\times 32\times 32\). Among the other ML-based methods applied (SVM, MLP, Bidirectional LSTM), the accuracy of 90.47% achieved by the CNN was the highest. However, the main drawback of this method is the increased memory requirement for the voxelized representation of the target information, which is not a concern when using micro-Doppler signatures. Figure 5: Convolutional layers.