## 2 Background and Related Literature
### Multivariate Anomaly Detection  
Rebuilding-based models: By reproducing the original input based on specific latent factors, it learns the illustration for the whole time series. It obtains the features from the unsupervised model by mapping the characteristics of an instance to integrated visible neurons, which are then employed by an autoencoder to reconstruct the features. GANs (Generative Adversarial Networks) are also commonly utilized in multivariate time series anomaly identification. A novel GAN-based anomaly detection approach is utilized in multivariate time-series anomaly detection that uses the GAN-trained discriminator as well as residuals between generator-reconstructed data and real samples. Unpredictable instances might cause deterministic techniques to fail; to solve this, stochastic models for multivariate time-series anomaly detection are utilized. To capture the common patterns behind data, it learns robust representations of multivariate time series with stochastic variable connection and planar normalizing flow. A pattern with a low modernization probability is considered an anomaly under their model. [PERSON] et al. [16] introduced the STOMP algorithm that improved the scalability of the motif discovery. The proposed algorithm produced illegal perceptions in seismology and other fields. [PERSON] and [PERSON] [17] proposed several techniques for optimizing self-joining using a GPU, which included a GPU-efficient index that employs a bounded search, a batching scheme to accommodate large result sets, and duplicate search removal with low overhead. In addition, they proposed a performance model that reveals the bottlenecks related to the result of a given data set size and enables the selection of a batch size that mitigates two sources of performance degradation. However, the proposed model fails to calculate the distance between points, and it degrades the performance of index searches when the search distance is increased. [PERSON] and [PERSON] [20] proposed an auto-distance covariance function for serial dependence evaluation to support the estimate residuals. The proposed method is based on time series model classification. The proposed method correctly identified misconfigurations when it was applied superfluously. However, the proposed model failed to justify the claimed idea. Furthermore, this process requires higher complexity. [PERSON] and [PERSON] [21] exploited a similarity threshold more aggressively to limit the set of candidate pairs that are considered to reduce the amount of information indexed initially. The proposed method is based on the discrete Fourier transform (DFT). However, the method is complex, with many parameters to adjust. Prediction-based models: Anomalies are detected based on prediction errors. These models use non-parametric thresholding and unsupervised features to evaluate predictions provided by the Long Short-Term Memory (LSTM) network. They develop an automated anomaly detection system to monitor the spacecraft's telemetry data. For multivariate time series, a real-time anomaly detection system based on Hierarchical Temporal Memory and Bayesian Network can also be utilized. Through an end-to-end learning framework, non-temporal dimensional reduction and recurrent auto-encoders may be used to handle the challenge of multivariate time series. [PERSON] and [PERSON] [22] proposed an efficientmethod to detect large-scale multimedia data using waveform similarity that overcomes the disadvantages of existing detection methods. The proposed mechanism consists of an efficient supervised multimodal hashing method that focuses on directly employing semantic labels to monitor the hashing learning process. [PERSON] [23] proposed the Partition-based Similarity Search (PSS) algorithm, which uses a static partitioning algorithm that places dissimilar vectors into different groups and balances the comparison workload with a circular assignment. [PERSON] et al.