# Time Series Anomaly Detection for KPIs Based on Correlation Analysis and HMM
## 5 Conclusions  
This paper proposes an anomaly detection method for KPIs based on correlation analysis and HMM. It can identify abnormal KPIs within a set period from a large number of KPIs in a system and the transfer state between them. In the anomaly detection method addressed in this paper, we first propose a 1D-CNN-TCN prediction model to predict the KPIs and obtain the residual sequence for screening the possible abnormal KPIs. This model combines CNN's local feature acquisition ability with TCN's temporally dependent feature acquisition ability to improve the prediction accuracy. The residual sequence of abnormal KPIs can highlight the abnormal segment in each KPI, such that the correlation analysis is not disturbed by the original fluctuation of KPIs, and thus the accuracy of the correlation analysis is improved. The experimental results show that the F1-score of the correlation analysis method in this paper is also the best. HMM parameters are confirmed according to the correlation matrix. After training the HMM, other KPIs that may cause a KPI anomaly are found, which reduces the time required for operation and maintenance staff to find a large number of abnormal KPIs. The results of the ablation experiment in this paper compared with the baseline method are relatively good, showing that it has certain advantages in analyzing the relationship between multiple abnormal indexes.  
The method in this paper can further determine the relationship of influence between KPIs by obtaining abnormal KPIs, which can help build a fault propagation diagram and help the operation and maintenance personnel to perform rapid troubleshooting. However, the method in this paper still has some limitations, and the specific threshold of the correlation analysis method still needs to be adjusted according to different environments. The HMM can only obtain the influence relationship of KPIs for adjacent times, and cannot determine the continuous influence relationship of multiple KPIs over a long time.  
There is still room for improvement in our research. Next, we will attempt to adjust the threshold adaptively, and optimize the acquisition of the relationship between KPIs.  
Z.S., conceptualization, methodology, investigation, validation, formal analysis, writing--original draft, writing--review and editing; Y.Z. ([PERSON]), funding acquisition, supervision, validation, formal analysis, writing--review and editing; X.Z., supervision, validation, formal analysis, writing--review and editing; Y.Z. ([PERSON]), investigation, validation, writing--original draft, writing--review and editing; Z.C., validation, formal analysis, writing--review and editing; X.W., investigation, formal analysis. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the National Key R&D Program of China (Grant No. 2018 YFB1601502), the Liao Ning Revitalization Talents Program (Grant No. XLYC1902071), and the Fundamental Research Funds for the Central Universities (Grant No. 3132019313).  
Not applicable.  
The data used to support the findings of this study are available from the corresponding author upon request.  
The authors would like to thank all anonymous reviewers and editors for their helpful suggestions for the improvement of this paper.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.