## 4 Experimental Design
### Experimental Settings  
In order to create the model, we used Tensorflow 1.14.0 and Python 3.7. We randomly selected 80% of the data to be the training set and 20% for the testing set. For the training phase, we set the hidden space Z of the VAE to two and the input dimension of the neuron unit of the hidden layer h to half. We apply the ReLU max(x, 0.1x) activation function and SGD optimizer to train the VAE. For the other parameters of the autoencoder, we use the default values. As described in Section 3.3, the anomaly score is determined in the testing phase, and the threshold is 95% of the root mean square error. Our experiments compare VAEGA with 9 outlier detection benchmark models, including OC-SVM [18], PCA [22], ABOD [41], HBOS [42], GAN [43], MOGAAL [44], DSEBM [28], AE [25], and pure VAE. PCA and OC-SVM are traditional outlier detection methods, ABOD and HBOS are distance-based methods to reflect the limitations of the distance of high-dimensional data space, and GAN and MOGAAL are outlier detection models based on generative adversarial networks. DSEBM, AE, and pure VAE are reconstruction-based outlier detection methods. For traditional methods such as PCA and OC-SVM, we use Scikit-Learn in TensorFlow to implement. For other methods besides the proposed VAEGA model, we use Tensorflow and python to implement them. The optimizer, learning rate, batch size and number of iterations used by the other methods are the same as those of the VAEGA model, except that the parameters of MOGAAL refer to the recommended settings of [1]. For comparability, AE, pure VAE and DSEBM share the same network structure and the same hidden layer units as VAEGA. The details of the baseline model are as follows:  
1. **Traditional outlier detection methods:** The OC-SVM method is a well-known kernel-based outlier detection method. Our experimental task uses the radial basis function (RBF) kernel, the abnormal rate \(\
u\) is set to 0.05, and uses the technique proposed by [18] to adjust the Gaussian kernel parameter \(\sigma\). PCA is a linear dimensionality reduction method that can be used to extract the main feature components of the data. The eigenvector matrix is compressed into h dimension, which is the same as the hidden space dimension of the VAE layer in the proposed method. PCA uses reconstruction error as an abnormal score. 2. **Distance-based:** The ABOD performance of the probabilistic method is significantly affected by the neighborhood size, and we set its parameter to 16 in comparative experiments. The HBOS method selects the number of commonly used neighbors as 10. 3. **Generative adversarial network-based methods:** In the comparative experiment, the GAN and VAEGA models basically have the same network structure, but the output layer of the discriminator in GAN is set to a one-dimensional structure. The configuration of MOGAAL can be found in [44]
4. **Reconstruction-based methods:** DSEBM is a deep-structured energy-based model, which is one of the recent deep-learning methods for unsupervised outlier detection. In DSEBM, the energy-based models (EBM) energy score of a sample is used as a criterion for detecting outliers. Autoencoder is an unsupervised nonlinear learning algorithm for data dimensionality reduction. The neural network parameters of the training encoder and decoder are the same. AE uses the error before and after reconstruction as an abnormality criterion. The training method, parameters, and the number of hidden layer units of pure VAE are the same as those of the VAEGA model. In the experiment, we search for abnormal subspaces using the Creditcard dataset, which has perfect data preprocessing for further evaluation of the model. The input of the GA layer is the set of outliers obtained through the outlier detection of the VAE layer. The GA layer starts with a population of 100, and the distance encoding is determined by the input dimension dim of the outlier. The fitness function calculates the SOD for each subspace.