# Detecting IoT Anomalies Using Fuzzy Subspace Clustering Algorithms
## 3 Proposed Methods
### Gustafson-Kessel (GK) Algorithm [42; 47]
The dataset sizes considered are 1,000,000, 2,000,000, 3,000,000, 4,000,000, and 4,898,431 records. The dimension of the dataset is taken as a constant. The methods are executed multiple times with the given sizes of the dataset, and the corresponding results are recorded and presented as a bar diagram in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{8}{c}{**\% of Attack Parameters**} \\ \hline
**Sl. NO.** & **Parameters** & **NT-FCM** & **NT-GK** & **NT-GG** & **NT-M-FCM** & **NT-CM-FCM** \\ \hline
1 & Denial of service & 78.3 & 81.33 & 82.99 & 87.96 & 94.83 \\ \hline
2 & Remote to local & 77.56 & 81.42 & 81.85 & 82.83 & 90.22 \\ \hline
3 & User to root & 53.50 & 58.89 & 60.80 & 63.89 & 68.91 \\ \hline
4 & Probe & 61.79 & 64.53 & 63.75 & 66.91 & 69.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative analysis of various attack parameters using Kitsune dataset. Figure 6: Comparative analysis of detection rates of 5 NT-based methods with KDDCup’99. Figure 8: Comparative analysis of false alarm rates of 5 NT-based methods with KDDCup’99. Figure 7: Comparative analysis of accuracy rates of 5 NT-based methods with KDDCup’99. Figure 10: Comparative analysis of detection rates of 5 NT-based methods with Kitsune dataset. Figure 9: Comparative analysis of percentage attack parameter of 5 NT-based methods with KDD-Cup’99. Figure 11: Comparative analysis of accuracy rates of 5 NT-based methods with Kitsune dataset. Figure 12: Comparative analysis of false alarm rates of 5 NT-based methods with Kitsune dataset. Figure 14: Comparative analysis of detection rates of all 10 algorithms with respect to dimensions of KDDCup’99. Figure 13: Comparative analysis of percentage attack parameter of 5 NT-based methods with Kitsune dataset. Figure 6:0 Comparative analysis of accurate rates of all 10 algorithms with respect to dimensions of KDDCup’99. Figure 6:1 Comparative analysis of detection rates of all 10 algorithms with respect to dimensions of Kitsune dataset. Figure 6:2 Comparative analysis of accurate rates of all 10 algorithms with respect to dimensions of Kitsune dataset. Figure 6:3 Comparative analysis of false alarm rates of all 10 algorithms with respect to dimensions of KDDCup’99. Figure 7 gives the accuracy rates of all the five NT-based fuzzy clustering methods with different sizes of the dataset KDDCup'99 [50]. Similar to the previous figure, dataset sizes considered are 1,000,000, 2,000,000, 3,000,000, 4,000,000, and 4,898,431 records, and the dimension of the dataset is taken as a constant. The methods are executed multiple times for the given sizes of the dataset, and the corresponding accuracy rates are recorded and presented as a bar diagram in Figure 6:4

Figure 8 displays the false alarm rates of all the five NT-based fuzzy clustering methods with different sizes of the dataset KDDCup'99 [50]. Similar to the detection and accuracy rates, the dataset sizes considered and the dimension of the dataset are taken as constants. The methods are executed multiple times with the given dataset sizes, and the corresponding false alarm rates are recorded and presented as a bar diagram in Figure 6:5

Table 3 presents the results obtained in terms of four attack parameters, namely denial of service, remote to local, user to root, and probe by NT-FCM, NT-GK, NT-GG, NT-M-FCM, and NT-CM-FCM clustering algorithms in tabular form. The dataset used here is KDDCup'99 [50]. It can easily be seen in the table that NT-CM-FCM outperforms the others, and the performances of the methods decreases from right to left. Figure 9 presents the results of Table 3 in a convenient way using a bar diagram. The algorithm NT-FCM is the least efficient, and NT-CM-FCM is the most efficient in terms of percentage of attack parameters. Figure 10 gives the detection rates of all the five NT-based fuzzy clustering methods with different sizes of the Kitsune dataset [51].