# An Incremental Local Outlier Detection Method in the Data Stream
## 3 Results
### Outlier Detection
Figure 10: ROC curves of kLOF and CLOF methods on the KDD Cup 1999 dataset with different \(k\) related to \(t\): (**a**) the ROC curves of kLOF method; (**b**) the ROC curves of CLOF method. Similar results also appeared in the analysis of the Shuttle data set, as shown in Figures 14-17. Due to the limit of space, only the experimental results are provided: the CNN-based method CLOF had better outlier detection performance and stability against \(n\) and \(k\) changing than the kNN-based method kLOF. Figure 14: ROC curves of kLOF and CLOF methods on the Shuttle dataset with different \(k\) related to \(t\): (**a**) the ROC curves of kLOF method; (**b**) the ROC curves of CLOF method. Figure 12: ROC curves of kLOF and CLOF methods on the KDD Cup 1999 dataset with different \(n\) related to \(t\): (**a**) the ROC curves of kLOF method; (**b**) the ROC curves of CLOF method. Figure 13: AUC values of kLOF and CLOF methods on the KDD Cup 1999 dataset with different \(n\) related to \(t\), and the box plots for kLOF and CLOF: (**a**) the AUC values of kLOF and CLOF methods; (**b**) the box plots for kLOF and CLOF methods. Figure 16: ROC curves of kLOF and CLOF methods on the Shuttle dataset with different \(n\) related to \(t\): (a) the ROC curves of kLOF method; (b) the ROC curves of CLOF method. Figure 17: AUC values of kLOF and CLOF methods on the Shuttle dataset with different \(n\) related to \(t\) and the box plots for kLOF and CLOF: (a) the AUC values of kLOF and CLOF methods; (b) the box plots for kLOF and CLOF methods. Figure 15: AUC values of kLOF and CLOF methods on the Shuttle dataset with different \(k\) related to \(t\) and the box plots for kLOF and CLOF: (a) the AUC values of kLOF and CLOF methods; (b) the box plots for kLOF and CLOF methods. The LWSNDR dataset is a time series type dataset from the Wireless Sensor Network. This dataset was different than the discrete data of the KDD Cup 1999 and Shuttle datasets; however, the proposed CLOF method had comparable outlier detection accuracy with the kNN-based kLOF method, as shown in Figure 18. However, due to the nonhomogeneity in LWSNDR dataset, the detection accuracy had obvious degradation in the moteid3 dataset when k was small, as shown in Figure 18c,d. This indicates that the parameter \(k\) and \(n\) should be optimized to obtain better detection accuracy, which can be summarized as the adaptive optimization of sliding window width problems. With the tests on three real-life datasets, the proposed CLOF method obtained better outlier detection performance than the kNN-based kLOF method. In many applications such as signal processing and intrusion detection of the network, It was very important to obtain high DR with low FPR. However, the DR and FPR were two conflicting factors, and DR increased with FPR. In the tests with different \(k\), when \(k\) increased and became close to \(n\), DR tended to increase quickly, and FPR tended to increase slowly. In the tests with different \(n\), when \(n\) increased away from \(k\), DR tended to increase slowly, and FPR tend to increase quickly. These results indicated that the maximum compromise of DR and FPR appeared when \(k\) was close to \(n\). The choice of \(k\) and \(n\) can be summarized as the optimization problem of sliding window width, which is another important research direction and will be researched in future studies.