## 6 Discussion
### Operational Complexity and Detection Limitations  
The operational cost depends on many factors, i.e., on the number of classes, the number of features, the number of samples, as well as on the choice of the corresponding LSM mapping and the _complexity_ of the current classification task. For instance, applying the SVM-Acc measure in combination with the BVDB led to the highest averaged operational time (AOT) _by far_ (see Table 7). The AOT for the BVDB in combination with the SVM-Acc mapping is approximately equal to 470 s, followed by the second longest AOT of approximately 20 s for the Mfeat data set. Note that the BVDB has less features than the Mfeat data set (194 to 649), and also consists of less classes (5 to 10). Obviously, the BVDB is composed of more data points than the Mfeat data set (8700 to 2000). However, on the other hand, the BVDB consists of fewer data points than the Nursery data set (8700 to 12,598), for which the AOT is only \(\sim\)2 s, in combination with the SVM-Acc measure. These observations emphasise that the operational cost depends indeed on the combination of all aforementioned factors, including the _complexity_ of the corresponding classification task. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Data Set** & **Cl** & **Fea** & **Sam** & **DR** & **SVM-Acc** \\ \hline Iris & 3 & 4 & 150 & \(0.25\pm 0.14\) & 19.97 \(\pm\) 3.02 \\ Seeds & 3 & 7 & 210 & 0.16 \(\pm\) 0.01 & 17.36 \(\pm\) 1.61 \\ CMC & 3 & 9 & 1473 & 0.34 \(\pm\) 0.11 & 1987.39 \(\pm\) 2.25 \\ Forests & 4 & 27 & 523 & 0.42 \(\pm\) 0.15 & 2267.25 \(\pm\) 4.47 \\ Vehicles & 4 & 18 & 846 & 0.43 \(\pm\) 0.04 & 9069.24 \(\pm\) 13.29 \\ LEV-4 & 4 & 4 & 1000 & 0.32 \(\pm\) 0.07 & 70.16 \(\pm\) 1.88 \\ SWD & 4 & 10 & 1000 & 0.34 \(\pm\) 0.02 & 110.61 \(\pm\) 1.71 \\ Cars & 4 & 6 & 1728 & 0.31 \(\pm\) 0.02 & 92.04 \(\pm\) 4.33 \\ Nursery & 4 & 8 & 12,958 & 1.76 \(\pm\) 0.14 & 2079.20 \(\pm\) 16.89 \\ ESL-5 & 5 & 4 & 488 & 0.29 \(\pm\) 0.02 & 52.81 \(\pm\) 1.91 \\ LEV & 5 & 4 & 1000 & 0.40 \(\pm\) 0.04 & 90.75 \(\pm\) 2.12 \\ BVDB & 5 & 194 & 8700 & 44.26 \(\pm\) 4.91 & 469,839.44 \(\pm\) 2608 \\ ERA-7 & 7 & 4 & 1000 & 1.09 \(\pm\) 0.09 & 539.96 \(\pm\) 5.43 \\ Segment & 7 & 19 & 2310 & 1.77 \(\pm\) 0.12 & 13,851.62 \(\pm\) 58.83 \\ ESL & 9 & 4 & 488 & 34.01 \(\pm\) 0.43 & 200.59 \(\pm\) 1.94 \\ ERA & 9 & 4 & 1000 & 77.50 \(\pm\) 2.56 & 616.12 \(\pm\) 1.61 \\ Mfeat & 10 & 649 & 2000 & 392.36 \(\pm\) 1.13 & 19,661.20 \(\pm\) 27.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Running Time Comparison. Cl: Number of Classes. Fea: Number of Features. Sam: Number of Samples. DR: Detection based on the discriminant ratio. SVM-Acc: Detection based on the linear SVM resubstitution accuracy. Depicted are the mean and standard deviation (std) values, for the operational time in ms, averaged over ten repetitions. For the SVM-Acc approach, for the BVDB data set, we removed the digits from the std value, for the sake of readability. Intuitively, the task of classifying different pain levels based on the participants' physiological signals, such as the heart rate (BVDB), obviously seems to be more complex than differentiating between ten digits based on features such as pixel averages (Mfeat). For instance, in one of our recent studies [29], we obtained the following accuracy values. For the Mfeat data set, we obtained an averaged cross-validation (CV) accuracy of \(\
eg 96\%\), including all 10 classes, in combination with bagging [30] and the early fusion approach [31]. In contrast, for the BVDB, including only two of the _best separable_ classes (no pain vs. the highest pain level), we merely obtained a mean CV accuracy of about \(82\%\) (with the same size for the test folds). Implementing SVM classifiers in combination with the BVDB, very likely leads to more support vectors, in comparison to training SVM classifiers based on the Mfeat data set. An increased amount of support vectors leads to an increased amount of updating steps, and thus to a greater training duration.