# Adaptive Seasonality Anomaly Detection Algorithm under Intricate KPI Profiles
## 2 Background and Related Work
### KPI Anomaly Detection Algorithm  
As discussed in Section 1, existing KPI anomaly detection algorithms shown in Table 1 are divided into three categories, including traditional statistical, supervised learning and unsupervised learning algorithms [11]. For traditional statistical algorithms, [PERSON], [PERSON] et al. [12] studied the problem of network attack detection based on ARIMA in 2010. In 2012, [PERSON], [PERSON] et al. [3] developed the end-to-end service quality evaluation problem based on Holt-Winter. In 2013, [PERSON], [PERSON] et al. [4] studied the view of web search response time based on TSD. The disadvantage of them is that they all need to input seasonal fitting parameters and cannot adapt to intricate KPI profiles. For supervised learning algorithms, in 2015 [PERSON], [PERSON] et al. [5] proposed Opperence based on traditional statistical algorithms to solve the problems of service quality monitoring and performance anomaly detection. In the same year, [PERSON] et al. [6] presented system anomaly monitoring based on traditional KPI anomaly detection methods. In 2019, [PERSON] et al. [13] designed an ensemble learning scheme based on extreme learning machine (ELM) algorithm and majority voting method to detect abnormal electricity consumption. In 2020, [PERSON] et al. [24] firstly discussed the anomaly detection in building energy consumption. It comprehensively introduced a method to classify existing algorithms based on different factors, such as the machine learning algorithm, feature extraction approach, detection level, computing platform, application scenario and privacy preservation. Then they introduced a new solution [14] to detect energy consumption anomalies. Besides micro-moment features extraction, they developed a deep neural network architecture for efficient abnormality detection and classification. In 2021, they also used the autoencoder and micro-moment analysis to detect abnormal energy usage [15]. To provide an explainable model, [PERSON] et al. [16] propose a novel Graph Deviation Network (GDN) approach. It can learn a graph of relationships between sensors, and detects deviations from these patterns. Similarly, [PERSON] et al. [17] presented a new framework for multivariate time series anomaly detection (GTA) that involves automatically learning a graph structure, graph convolution and modeling temporal dependency using a Transformer-based architecture. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Time** & **Type** \\ \hline [PERSON], [PERSON] et al. [12] & 2010 & traditional statistical \\ [PERSON], [PERSON] et al. [3] & 2012 & traditional statistical \\ [PERSON], [PERSON] et al. [4] & 2013 & traditional statistical \\ \hline [PERSON], [PERSON] et al. [5] & 2015 & supervised learning \\ [PERSON] et al. [6] & 2015 & supervised learning \\ [PERSON] et al. [13] & 2019 & ensemble learning \\ [PERSON] et al. [14] & 2020 & deep neural network \\ [PERSON] et al. [15] & 2021 & deep neural network \\ [PERSON] et al. [16] & 2021 & graph deviation network \\ [PERSON] et al. [17] & 2021 & transformer-based architecture \\ [PERSON] et al. [18] & 2021 & federated learning \\ \hline [PERSON], [PERSON] et al. [19] & 2018 & unsupervised VAE \\ [PERSON] et al. [20] & 2021 & unsupervised temporal autoencoder \\ [PERSON] et al. [21] & 2021 & unsupervised learning \\ [PERSON] et al. [22] & 2021 & fast unsupervised learning \\ [PERSON] et al. [23] & 2021 & unsupervised learning \\ \hline \hline \end{tabular}
\end{table} 
Table 1: KPI Anomaly Detection Algorithms. Recently, [PERSON] et al. [18] put forward an anomaly detection framework. Firstly, this captures more detailed data regarding the time series' shape and morphology characteristics. Then, it utilizes interval representation to realize data visualization and mine the internal relationships. However, these supervised methods are unable to adapt to intricate KPI profiles due to the inherent lack of labeled anomalies in historical data. For unsupervised learning algorithms, in 2018 [PERSON], [PERSON] et al.