
## 7. Experiments And Discussion

For Algorithm 1, because each point should be evaluated by any other two ones, time consumption is O(N
3) when number of data is N. But since each evaluating pairs are isolated, this algorithm is parallel, which makes it possible to be run in O(N). Correspondingly, algorithm 1" can be done in O(N
1) time (>0), and in parallel condition, it decreases to O(N ). 

Robust simple regression, e.g. LTS, requires sorting of the squared residuals, which takes O(*NlogN* ) operations (Rousseeuw, 1984). Considering operations needed by whole subsamples in data is N
2, total operations is O(N
3*logN* ). 

Algorithm 2 can be done in O(N
2T ) time. Algorithm 4 can be done in O(N
3T ) time and in O(N
2T ) time in parallel way. 

Following experiments are based on Algorithm 4. Original sine data are got from function y  sin(2x 47), x is an integer in [0,47]. Outlier patches are introduced, size -1 to the x: 7, 8, 9, 10, and size +2 to the x index 28, 29, 30, 31, 32. Result is in Fig. 2. Table 4 lists corresponding RDD values of related points. The first point whose IIR value is greater than 1.81 is index 10, so all points above 10 (whose RDD values are greater than that of index 10) are confirmed as outliers. We see all outliers are correctly detected. T is equal to 2 here.

![0_image_0.png](0_image_0.png)

1 2
Three types of real time series data, which are measured every 30 minutes from 0 to 24 hours, are listed in Fig. 3, Fig. 4, and Fig. 5. One is CO2 flux data, one is sensible heat flux data, the other is latent heat flux data. Both achieved from Yucheng station, China.