# Research on the Fastest Detection Method for Weak Trends under Noise Interference

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Sliding Window

#### 2.2. Extrapolation of Online Data Segmentation

## 3. Sliding Nested Fastest Trend Anomaly Detection Algorithm

Algorithm 1 Sliding Nest Window Weights Changed Algorithm |

SNWWCA: initialize LW, SWSet weights range: (a, b) Compute weights step: (b − a)/LW; (b − a)/SW; Update: t; Update: P * (b − a)/LW; S * (b − a)/SW; Update: P * (b − a)/LW; S * (b − a)/SW; |

Algorithm 2: SNWFD-DS |

DCUSUM-DS: initialize LW, SW, T, $\beta $Compute weights of SW and LW Compute: $med{S}_{x}$, $std{S}_{x}$, $med{L}_{x}$, $std{L}_{x}$ $Di{f}_{-}ma=med{S}_{x}-med{L}_{x}$ Compute: $Di{f}_{-}m{a}_{-}mean{S}_{Di{f}_{-}ma}$, $Di{f}_{-}m{a}_{-}mean{L}_{Di{f}_{-}ma}$, $Di{f}_{-}m{a}_{-}std{S}_{Di{f}_{-}ma}$, $Di{f}_{-}m{a}_{-}std{L}_{Di{f}_{-}ma}$ $Di{f}_{-}m{a}_{-}result=Di{f}_{-}m{a}_{-}mean{S}_{Di{f}_{-}ma}-Di{f}_{-}m{a}_{-}mean{L}_{Di{f}_{-}ma}$ Compute: $Di{f}_{-}m{a}_{-}meanS$, $Di{f}_{-}m{a}_{-}meanL$, $Di{f}_{-}m{a}_{-}stdS$ Whether $Di{f}_{-}m{a}_{-}result>0$ Compute: $\mathrm{sum}(Di{f}_{-}m{a}_{-}result)$ Compute: $\mathrm{Re}sult=Di{f}_{-}m{a}_{-}meanL*\mathrm{abs}(\mathrm{sum}(Di{f}_{-}m{a}_{-}result))$ Box(Score(Result)) Whether Score > $\beta $ Output: label VA |

## 4. Real Data Verification

^{®}) Core(™) i5-4570 @ 3.2 GHz 3.2 GHz, the memory was 16 G, and the operating system was Window10 64-bit.

## 5. Discussion

## 6. Discussion, Implication, and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wu, W.; He, L.; Lin, W. Local trend inconsistency: A prediction-driven approach to unsupervised anomaly detection in multi-seasonal time series. arXiv
**2019**, arXiv:1908.01146. [Google Scholar] - Chen, R.Q.; Shi, G.H.; Zhao, W.L.; Liang, C.H. A Joint Model for Anomaly Detection and Trend Prediction on IT Operation Series. arXiv
**2019**, arXiv:1910.03818. [Google Scholar] - Li, G.; Wang, J.; Liang, J.; Yue, C. Application of sliding nest window control chart in data stream anomaly detection. Symmetry
**2018**, 10, 113. [Google Scholar] [CrossRef] [Green Version] - Yassine, H.; Ghanem, K.; Alsalemi, A.; Bensaali, F.; Amira, A. Artificial intelligence based anomaly detection of energy consumption in buildings: A review, current trends and new perspectives. Appl. Energy
**2021**, 287, 116601. [Google Scholar] - Gao, J.; Song, X.; Wen, Q.; Wang, P.; Sun, L.; Xu, H. RobustTAD: Robust time series anomaly detection via decomposition and convolutional neural networks. arXiv
**2020**, arXiv:2002.09545. [Google Scholar] - Liu, X.; Lai, Z.; Wang, X.; Huang, L.; Nielsen, P.S. A Contextual Anomaly Detection Framework for Energy Smart Meter Data Stream. In Proceedings of the International Conference on Neural Information Processing, Bangkok, Thailand, 18–22 November 2020; Springer: Cham, Switzerland, 2020; pp. 733–742. [Google Scholar]
- Cavaglia, M.; Staats, K.; Gill, T. Finding the origin of noise transients in LIGO data with machine learning. arXiv
**2018**, arXiv:1812.05225. [Google Scholar] [CrossRef] [Green Version] - Hasan, M.; Orgun, M.A.; Schwitter, R. Real-time event detection from the Twitter data stream using the TwitterNews+ Framework. Inf. Process. Manag.
**2019**, 56, 1146–1165. [Google Scholar] [CrossRef] - Gomes, H.M.; Bifet, A.; Read, J.; Barddal, J.P.; Enembreck, F.; Pfharinger, B.; Holmes, G.; Abdessalem, T. Adaptive random forests for evolving data stream classification. Mach. Learn.
**2017**, 106, 1469–1495. [Google Scholar] [CrossRef] - Tang, F.; Mao, B.; Fadlullah, Z.M.; Kato, N.; Akashi, O.; Inoue, T.; Mizutani, K. On removing routing protocol from future wireless networks: A real-time deep learning approach for intelligent traffic control. IEEE Wirel. Commun.
**2017**, 25, 154–160. [Google Scholar] [CrossRef] - Ribeiro, D.; Mateus, A.; Miraldo, P.; Nascimento, J.C. A real-time deep learning pedestrian detector for robot navigation. In Proceedings of the 2017 IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC), Coimbra, Portugal, 26–28 April 2017; pp. 165–171. [Google Scholar]
- Mao, B.; Tang, F.; Fadlullah, Z.M.; Kato, N. An intelligent route computation approach based on real-time deep learning strategy for software defined communication systems. IEEE Trans. Emerg. Top. Comput.
**2019**. [Google Scholar] [CrossRef] - Meyer, A.; Zverinski, D.; Pfahringer, B.; Kempfert, J.; Kuehne, T.; Sündermann, S.H.; Stamm, C.; Hofmann, T.; Falk, V.; Eickhoff, C. Machine learning for real-time prediction of complications in critical care: A retrospective study. Lancet Respir. Med.
**2018**, 6, 905–914. [Google Scholar] [CrossRef] - Xu, B.; Rathod, D.; Yebi, A.; Filipi, Z. Real-time realization of Dynamic Programming using machine learning methods for IC engine waste heat recovery system power optimization. Appl. Energy
**2020**, 262, 114514. [Google Scholar] [CrossRef] - Thomson, D.J.M.; Barclay, D.R. Real-time observations of the impact of COVID-19 on underwater noise. J. Acoust. Soc. Am.
**2020**, 147, 3390–3396. [Google Scholar] [CrossRef] [PubMed] - Wang, W.; Zhang, M. Data Stream Adaptive Partitioning of Sliding Window Based on Gaussian Restricted Boltzmann Machine. In Artificial Intelligence in China; Springer: Singapore, 2020; pp. 220–228. [Google Scholar]
- Leung, C.K.S.; Jiang, F.; Hayduk, Y. A landmark-model based system for mining frequent patterns from uncertain data streams. In Proceedings of the 15th Symposium on International Database Engineering & Applications, Lisbon, Portuga, 21–27 September 2011; pp. 249–250. [Google Scholar]
- Krämer, J.; Yang, Y.; Cammert, M.; Seeger, B. Dynamic plan migration for snapshot-equivalent continuous queries in data stream systems. In Proceedings of the International Conference on Extending Database Technology, Munich, Germany, 26–31 March 2006; Springer: Berlin/Heidelberg, Germany, 2006; pp. 497–516. [Google Scholar]
- Du, P.; Hamdulla, A. Infrared Small Target Detection Based on Facet-Kernel Filtering Local Contrast Measure. In Proceedings of the China Conference on Wireless Sensor Networks, Chongqing, China, 12–14 October 2019; Springer: Singapore, 2019; pp. 360–367. [Google Scholar]
- Li, H.; Wu, X.J.; Kittler, J. RFN-Nest: An end-to-end residual fusion network for infrared and visible images. Inf. Fusion
**2021**, 73, 72–86. [Google Scholar] [CrossRef] - Riss, G.; Romano, M.; Memon, F.A.; Kapelan, Z. Detection of water quality failure events at treatment works using a hybrid two-stage method with CUSUM and random forest algorithms. Water Supply
**2021**. [Google Scholar] [CrossRef] - Li, G.; Wang, J.; Liang, J.; Yue, C. The application of a double CUSUM algorithm in industrial data stream anomaly detection. Symmetry
**2018**, 10, 264. [Google Scholar] [CrossRef] [Green Version] - Meng, M.; Wang, L.; Shang, W. Decomposition and forecasting analysis of China’s household electricity consumption using three-dimensional decomposition and hybrid trend extrapolation models. Energy
**2018**, 165, 143–152. [Google Scholar] [CrossRef] - Colonna, M.; Danzon, A.; Delafosse, P.; Mitton, N.; Bara, S.; Bouvier, A.-M.; Ganry, O.; Guizard, A.-V.; Launoy, G.; Molinie, F.; et al. Cancer prevalence in France: Time trend, situation in 2002 and extrapolation to 2012. Eur. J. Cancer
**2008**, 44, 115–122. [Google Scholar] [CrossRef] [PubMed] - Ma, J.; Ding, Y.; Cheng, J.C.P.; Jiang, F.; Wan, Z. A temporal-spatial interpolation and extrapolation method based on geographic Long Short-Term Memory neural network for PM
_{2.5}. J. Clean. Prod.**2019**, 237, 117729. [Google Scholar] [CrossRef] - Liang, H.; Song, L.; Wang, J.; Guo, L.; Li, X.; Liang, J. Robust unsupervised anomaly detection via multi-time scale DCGANs with forgetting mechanism for industrial multivariate time series. Neurocomputing
**2021**, 423, 444–462. [Google Scholar] [CrossRef]

Algorithm | Length of Short Window | Length of Long Window | Threshold | Out Rate | Weights |
---|---|---|---|---|---|

SNWCAD–DS | 80 | 400 | 0.4 | 8 | 0.0125/0.0025 |

DCUSUM–DS | 80 | 400 | 0.4 | 8 | 0.0125/0.0025 |

SNWFD–DS | 80 | 400 | 0.4 | 8 | (0:0.003:0.0253)/ (0:0.0001:0.005) |

Setting of Short Window | DCUSUM-DS | SNWCAD-DS | SNWFD-DS |
---|---|---|---|

20 | 0.2718 | 0.2254 | 0.2931 |

40 | 0.2823 | 0.2391 | 0.3072 |

60 | 0.2919 | 0.2508 | 0.3246 |

80 | 0.3077 | 0.2640 | 0.3384 |

100 | 0.3204 | 0.2764 | 0.3565 |

120 | 0.3358 | 0.2912 | 0.3718 |

140 | 0.3441 | 0.3047 | 0.3867 |

160 | 0.3586 | 0.3269 | 0.3996 |

180 | 0.3760 | 0.3416 | 0.4129 |

200 | 0.3862 | 0.3587 | 0.4276 |

average | 0.3238 | 0.2879 | 0.3618 |

Setting of Short Window | SNWCAD-DS | DCUSUM-DS | SNWFD-DS |
---|---|---|---|

20 | 9 | 11 | 8 |

40 | 12 | 22 | 10 |

60 | 14 | 31 | 12 |

80 | 15 | 42 | 13 |

100 | 18 | 53 | 15 |

120 | 17 | 62 | 16 |

140 | 20 | 74 | 17 |

160 | 23 | 82 | 19 |

180 | 25 | 93 | 20 |

200 | 28 | 105 | 21 |

average | 18.1 | 57.5 | 15.1 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, G.; Liang, J.; Yue, C.
Research on the Fastest Detection Method for Weak Trends under Noise Interference. *Entropy* **2021**, *23*, 1093.
https://doi.org/10.3390/e23081093

**AMA Style**

Li G, Liang J, Yue C.
Research on the Fastest Detection Method for Weak Trends under Noise Interference. *Entropy*. 2021; 23(8):1093.
https://doi.org/10.3390/e23081093

**Chicago/Turabian Style**

Li, Guang, Jing Liang, and Caitong Yue.
2021. "Research on the Fastest Detection Method for Weak Trends under Noise Interference" *Entropy* 23, no. 8: 1093.
https://doi.org/10.3390/e23081093