## 2 Related Work
[PERSON] and [PERSON] [28] proposed methods based on variational encoders used for high-dimensional data outlier detection. Here, a hidden space probability and a reconstruction error probability are combined to produce an outlier score, and a binary clustering method is used to separate potential normal instances from outliers. VAE has been used in a wide range of applications to deal with outlier detection problems, and [29] is one example in which detecting high-dimensional false news information was tackled with the use of the latent space of a variational autoencoder. Another application involved using a different recurrent neural network and variational autoencoder network (RNN-VAE) architecture [30] to identify outliers in time series data. VAE has also been widely adopted for intrusion detection and internet monitoring [31]. Image and video outlier detection problems [32] can also employ VAE successfully in their applications. In practical applications, to realize a better interpretation of the detected outliers, it is vital to identify and obtain abnormal information about the outliers. The autoencoder deep neural network (ADNN) model [33] is based on the multi-objective autoencoder to extract the information features of high-order data for fault detection. Their ADNN-based, multi-objective autoencoder model extracts the information features of high-order data for fault detection. Another model in [33] utilizes k-nearest neighbors to capture anomalous locations for each row of output scores and utilizes abnormal scores to assess the intensity of the damage. However, capturing abnormal regions using full space traversal is exceedingly expensive, and an efficient method is required. Thus, genetic algorithms, a popular heuristic approach, have been employed to efficiently search for abnormal subspaces for each detected outlier by simulating biological or natural principles [34; 35; 36; 37]. [PERSON] et al. [38] proposed a genetic algorithm-based technique to identify outliers embedded in the subspace and use the bit freezing method to accelerate convergence. The GA-OCStuM model proposed in [39] is used for intelligent outlier detection in the Internet of Things, in which GA is used to optimize the selection of parameters during the training of the outlier detection model. [PERSON] et al. [40] propose an incremental outlier detection method and use a genetic algorithm to optimize the training parameters in order to improve DAE classification accuracy. A genetic algorithm is used in these methods to optimize and improve the outlier detection model. However, it does not significantly improve outlier detection and interpretation. Figure 1: A comparison of linear and nonlinear dimension reduction. While most of these methods have their advantages and can detect outliers, our approach provides an alternative solution to address some of the shortcomings stated in the existing methods in order to detect outliers not only effectively but with good interpretation. For instance, with an increasing dataset and dimension, some of the methods decrease in performance. Furthermore, exponential growth in the number of subspaces results in severe limitations in practical applications. The technique that adopts GA to tackle outlier detection and interpretation could not significantly show better interpretation when compared to our method. In this paper, we have combined VAE and GA to collectively leverage their advantages in detecting outliers effectively and offer good interpretations of the outlier detection results through abnormal subspace detection.