## 5 Conclusions and Future Work  
In this work, we have applied the SPLR model to achieve discriminative feature selection and subsequently improve attack classification for intrusion detection system (IDS). The first and major contribution of this work is to address high-dimensional datasets. The proposed method controls overfitting and feature redundancy by simultaneously carrying out the feature selection and classification. This enables the investigation of detailed discriminative features. Secondly, the proposed  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Size of Training** & **Size of Testing** & **DR (\%)** & **Train** & **Average Training** \\  & **Datasets** & **Datasets** & **Time (s)** & **Time per Sample (s)** \\ \hline SVM [32] & 1,132,365 & 73,247 & 57.6 & 62,424 & 18.14 \\ GP [33] & 24,780 & 311,028 & 96.7 & 6480 & 0.2615 \\ ANN [12] & 4947 & 3117 & 92.27 & 780 & 0.1576 \\ MARS [34] & 11,982 & 11,982 & 96.46 & 30.66 & 0.0025 \\ Naive Bayes [35] & 65,525 & 65,525 & 95 & 1.89 & 0.0013 \\ I T I [36] & 169,000 & 311,029 & 92.38 & 18 & 0.00002 \\ PD Tree [37] & 444,458 & 49,384 & 46.67 & 48.8 & 0.00002 \\ K-Means [38] & 55,000 & 25,000 & 86 & 13 & 0.00002 \\ Apriori [35] & 44,458 & 49,384 & 87.5 & 18.94 & 0.000005 \\
**SPLR** & 1,074,985 & 67,688 & 97.65 & 11.6 & 0.000001 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance Comparison of SPLR with other classifier models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Size of Training** & **Size of Testing** & **DR (\%)** & **Train** & **Average Training** \\  & **Dataset** & **Dataset** & **Time (s)** & **Time per Sample (s)** \\ \hline VFDT [19] & 1,074,985 & 67,688 & 93.83 & 39.88 & 0.000003 \\
**SPLR** & 1,074,985 & 67,688 & 97.65 & 11.6 & 0.000001 \\ Bayes Net [29] & 49,596 & 15,437 & 90.62 & 6.28 & 0.00001 \\ J48 [29] & 49,596 & 15,437 & 92.06 & 15.85 & 0.00003 \\ LBK [29] & 49,596 & 15,437 & 92.22 & 10.63 & 0.00002 \\ C4.5 [30] & 49,596 & 15,437 & 92.06 & 15.85 & 0.0003 \\ Fuzzy Logic [31] & 49,596 & 15,437 & 91.65 & 192.16 & 0.0038 \\
**SPLR** & 49,596 & 15,437 & 98.26 & 7.5 & 0.000001 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental performance comparison of SPLR with other classifier models.  
classifier has been compared to state-of-the-art algorithms. The SPLR method shows some impressive characteristics and encouraging results. Our experimental results suggest that classification with the proposed feature selection method performs better than other classification models. The sparse model allows the combination of feature selection and classification into a unified framework by minimizing the combined empirical loss and penalization on the sparsity of feature variables. As a result, the running times of the SPLR method are linear with respect to the training samples and feature variables. The feature selection and prediction cost are also better than other methods suggested in the literature on the subject.  
As a future work, we think that the promising results of our experiments encourage for carrying out further research into the effects of different classifiers as well as the exploration of recent developments in the IDS domain.