## 2 Related Work  
Full-spatial outlier detection techniques based on statistics, clustering and classification have been extensively studied recently with implementation in algorithms such as Gaussian mixture model (GMM) [14], k-nearest neighbor (KNN) [15], local outlier factor algorithms (LOF) [16], cluster-based intelligence ensemble learning (CIEL) [17], one-class support vector machine (OC-SVM) [18] etc. In theory, conventional full-spatial outlier analysis can provide a suitable method for dealing with high-dimensional data. However, when considered in practice, with increasing dataset and dimension, the complexity in computation and time increases exponentially, which drastically decreases performance. Another set of algorithms available for high-dimensional data outlier detection is mostly concerned with methods of overcoming the limitations that exist in high-dimensional datasets. These outlier detection methods focus on subspace selection, data dimensionality reduction, and reconstruction. The methods can be categorized into two types: feature selection-based and feature transformation-based [19]. The feature selection method, also referred to as subspace outlier detection [20], is based on detecting outliers in a certain feature subset. The integrated strategy HiCS method in [21] identifies outliers by finding the high-contrast subspace projection of data and summarizing the outliers in each subspace. It involves the selection of subspaces along with calculating the outlier degree. This poses a computational challenge with exponential growth in the number of subspaces and, as a result, has a severe limitation in practical applications. The approach based on feature transformation, also referred to as dimensionality reduction, is typically employed to alleviate the issues related to the curse of dimensionality. Two approaches are used to tackle this issue. The first approach is to map the high-dimensional data to a lower dimension and then apply a conventional full-space outlier detection method to identify outliers. The second approach is to provide an effective way to reconstruct outliers from low-dimensional projections and to provide a way to capture the normal patterns. This allows for the separation of outliers and inliers by using the feature space of different dimensions effectively. Several outlier detection methods have been proposed utilizing this idea. A multivariate scheme for network anomaly detection based on principal component analysis (PCA) was proposed by [PERSON] [22]. PCA has a high time and calculation cost in calculating the covariant matrix and so can be limited to a linear transformation. [PERSON] et al. [23] used a support vector machine (SVM) to learn to distinguish the boundary between a high-density distribution and a low-density distribution and used the low-density distribution area data as outliers because of the difficulty in obtaining labeled outlier samples. [PERSON] and [PERSON], respectively, proposed methods based on one-class support vector machine (OC-SVM) [18] and support vector data description (SVDD) [24], making full use of normal data labeled for outlier detection. Some major challenges in this approach are finding parameter values to measure the size of the normal data area boundary in the feature space and to reduce the intensive computational cost associated with the kernel function calculation. A method that does not use linear combination was proposed by [PERSON] et al. [25], in which an autoencoder (AE) derived from nonlinear dimensionality reduction is used to detect outliers. As can be seen in Figure 1, the effects of AE and PCA show similar results, with AE showing better performance with nonlinear activation function. Therefore, in 2014, a method using a variation autoencoder was proposed by [PERSON] and [PERSON] [26]. Here, a variational inference is used to provide restrictions during the encoding stage to ensure that the generated vector follows a standard normal distribution. VAE is easier to generalize than AE [27].