gorithms
This section provides a sensitivity analysis for the proposed algorithms. Firstly, the intent is to study and compare the effectiveness of the proposed algorithms for the purpose of exposing outlier data. Then, the study will compare the size of candidate granules by applying each of the algorithms.
Table 7.6 shows a comparison of the results obtained by the proposed algo- rithms. As can be seen from Table 7.6, the Centroid Granule CG2, where the
Table 7.6: The Proposed Algorithms Results for synthetic dataset-5000 Top N GBOD RWDT CG1 CG2 5 4 4 3 4 10 7 7 6 8 15 12 12 9 12 20 16 16 13 16 25 19 19 16 19 30 23 23 19 24 35 25 25 22 27 40 28 28 25 31 45 32 32 28 35 50 37 37 32 39
CG is computed from the HG, outperforms the other GBOD, RWDT, CG1 algo- rithms. This is particularly the case from the Top 30 and upward as the accuracy of the CG2 is higher than that for the other algorithms. For example, when the top N was 50, the CG2 returns 39 true outliers and 11 falsely predicted points. Whereas, the GBOD, RWDT returns the same result: 37 with 13 falsely pre- dicted. The worst result for this data set was that given by the CG1 algorithm, with 32 true outlier points and 18 falsely predicted points.
The Figure7.17shows the precision of the proposed algorithms with different selected Top N.
Figure7.18, illustrates the trade-off between the false and true positive rates for the proposed algorithms.
Additionally, the study examines the effectiveness of the results that were acquired using the proposed algorithms to evaluate the real Breast Cancer Wis- consin dataset. Figure 7.19 shows the results comparatively.
From examination of both the synthetic and real datasets in figures 7.18 and
Figure 7.17: The Proposed Algorithms with Different Top N for Synthetic dataset-5000
Figure 7.19: ROC for the Proposed Algorithms for Synthetic dataset-5000 than the algorithms: RWDT, CG1 and GBOD. However, the gap between the proposed algorithms reduces when these algorithms are applied to a real dataset, as shown in Figure 7.19.
The study also investigates the number of granules in LG that are expected to
hold outlier data. Since the traditional DT table relies on the degree of support to determine HG and LG granule as in GBOD algorithm, the size of the LG set
which is likely to hold outlier data is significantly large compared to the HG set.
This reduces the efficiency of the proposed GBOD when detecting outlier. This is particularly the case when the dataset has very few numeric attributes, because finding granularity in a dataset with numeric attributes can be difficult.
For example, Figure GBODdistrbution illustrates the granule distribution based on the support degree for the Adult dataset using GBOD algorithm. As can be seen in the Figure GBODdistrbution, the size of the LG set is very large,
covering 91.5% granules. Whereas, the size of the HG is very small covering 8.5%
Figure 7.20: Distribution of the GBOD for Adult Dataset
Figure 7.22: Distribution of the GBOD for Breast Cancer Wisconsin dataset To overcome the limitations resulting from using the GBOD algorithm, and to reduce the mining space LG set, this study introduces the RWDT algorithm.
With the RWDT algorithm, the total weight of the granule is utilised to identify the HG and LG granules. For example, Figure RWDTdistrbution, illustrating
RWDT distribution, shows the granules’ distribution based on the total weight, as described by the RWDT algorithm for the Adult dataset. It is evident from the figure that the size of the LG in RWDT is very small compared to that using
GBOD, at 44.7%. This means that the RWDT algorithm mines just 44.7% of the data to find the outliers. Whereas, the GBOD algorithm mines 91.5% of the data for the same purpose.
As mentioned above, this study populates the distribution of another real dataset, called the Breast Cancer Wisconsin dataset to compare the differences between the LG from the GBOD and the LG LG from the RWDT, as described
in Figures 7.22 and 7.23 respectively.
Figure 7.23: Distribution of the RWDT for Breast Cancer Wisconsin dataset f the data as shown in Figure7.22. Unlike the GBOD, the number of granules, LG
that are likely to hold outlier values based on RWDT is 29% of the original dataset size (see Figure 7.23). Mining such small candidate granules LG from RWDT has
great advantages as the mining space is much smaller than the mining space in the GBOD algorithm.
In the case of the CG algorithm, all the HG granules are represented by a
single granule. Instead of computing the distance from the LGgranule to number
of HG to determine the similarity or deviation degree, the CG algorithm only
uses a single granule to represent all HG granules. The CG algorithm computes
Table 7.7: Decision Rules for D1 and D2 Database D1 D2 Original 73 67 5% 277 286 10% 376 373 15% 495 472