## 3 Results
### On Real-world Proteomic Data
#### Experiment #1: Protein Function Classification
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Class** & \(\boldsymbol{\alpha}\) & **ACC** & **SPC** & **SNS** & **NPV** & **PPV** & **Sparsity** \\ \hline \multirow{4}{*}{1} & 0.5 & 95.3 & 96.5 & 87.1 & 98.2 & 77.7 & **3.3** \\  & 1 & **97** & **98.4** & **87.3** & **98.3** & **88** & 16 \\  & 0.5 & 92.7 & 94.2 & **86.7** & **96.5** & 79.6 & **4.5** \\  & 1 & **94.5** & **97.3** & 83.8 & 95.9 & **88.9** & 22.7 \\  & 0.5 & 92.1 & 93.8 & **84.4** & **96.3** & 76.2 & **4** \\  & 1 & **93.3** & **95.5** & 83.9 & **96.3** & **81.9** & 17.4 \\  & 0.5 & 96.6 & 97.7 & **82.5** & **98.7** & 72.9 & **2.8** \\  & 1 & **97.3** & **98.6** & 79.8 & 98.5 & **81.6** & 7.8 \\  & 0.5 & 96.9 & 97.8 & **71.7** & **99** & 56.9 & **1.8** \\  & 1 & **97.9** & **98.9** & 70.4 & 98.9 & **75.3** & 5.1 \\  & 0.5 & 97.5 & 97.9 & **88.8** & **99.4** & 71.5 & **2.2** \\  & 1 & **98.7** & **99.4** & 86.2 & 99.3 & **87.8** & 9.6 \\  & 0.5 & 86.6 & 89.9 & 80.1 & 89.9 & 80.5 & **4.8** \\  & 1 & **88.8** & **91.6** & **83.4** & **91.6** & **83.6** & 36.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average results (in percentage) on Test Set for \(\ell_{1}\)-SVM. In bold, the best between the two fitness function tradeoff values for \(\alpha\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Class** & \(\boldsymbol{\alpha}\) & **ACC** & **SPC** & **SNS** & **NPV** & **PPV** & **Sparsity** \\ \hline \multirow{4}{*}{1} & 0.5 & 96.8 & 99 & 80.4 & 97.4 & 92 & **9.9** \\  & 1 & **97.2** & **99.2** & **81.9** & **97.6** & **93.6** & 11.5 \\  & 0.5 & 93.9 & 98 & 77.8 & 94.5 & 90.9 & **6.8** \\  & 1 & **94.5** & **98.3** & **79.7** & **95** & **92.2** & 26.1 \\  & 0.5 & 94 & **98.5** & 74.3 & 94.3 & 92.1 & **6.8** \\  & 1 & **94.7** & **98.5** & **78.2** & **95.1** & **92.3** & 18.6 \\  & 0.5 & 97.3 & 99.3 & **69.6** & **97.8** & 88.4 & **12.8** \\  & 1 & **97.3** & **99.4** & 69.2 & **97.8** & **89.9** & 19.1 \\  & 0.5 & 98.5 & 99.8 & 61.3 & 98.6 & 93 & **13.6** \\  & 1 & **98.7** & **99.9** & 63.8 & **98.7** & **97.1** & 31.7 \\  & 0.5 & 98.9 & **99.9** & 80.3 & 99 & 97.1 & **23.3** \\  & 1 & **99.1** & **99.9** & **83.5** & **99.2** & **97.2** & 28.7 \\  & 0.5 & **87.4** & 93 & **76.5** & **88.6** & 84.7 & **6.5** \\  & 1 & **87.4** & **93.4** & 75.7 & 88.3 & **85.3** & 6.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average results (in percentage) on Test Set for \(\
u\)-SVM. In bold, the best between the two fitness function tradeoff values for \(\alpha\). From Table 2 it is possible to see that when switching from \(\alpha=1\) to \(\alpha=0.5\), other than selecting a smaller number of symbols, \(\ell_{1}\)-SVMs tend to improve in terms of SNS and NPV for almost all classes. Similarly, from Table 3, it is possible to see that, when switching from \(\alpha=1\) to \(\alpha=0.5\), \(\
u\)-SVMs mainly benefit in terms of feature selection, with only class 7 showing minor performance improvements in terms of SNS and NPV. By comparing the two classification systems (i.e., by matching Tables 2 and 3) it is possible to draw the following conclusions:  
* at \(\alpha=1\): \(\ell_{1}\)-SVMs outperform the kernelised counterpart in terms of SNS (all classes) and NPV (all classes), whereas \(\
u\)-SVMs outperform the former in terms of SPC (all classes) and PPV (all classes). The overall ACC sees \(\ell_{1}\)-SVMs outperforming \(\
u\)-SVMs only for class 7, the two classifiers perform equally for classes 2 and 4 and for the remaining classes \(\
u\)-SVMs perform better.