## 4 Experimental Results
### WP-SVM Specificity and Storage Requirements  
Because CTC CAD data are often highly unbalanced with respect to the size of the classes TP1, TP2, and FP, the confusion rate does not fully demonstrate the effectiveness of _WP-SVM_, we therefore investigated the sensitivity of _WP-SVM_ in detecting polyps while the penalty factors \(\zeta\) and \(\lambda\) were varied. The main fallout in classification accuracy occurred between classes TP1 and TP2. The _WP-SVM_ identified the FP class correctly but failed to reach 100% detection sensitivity in the classes TP1 and TP2. This is not surprising considering that these classes are not completely linearly separable and that kernel functions were not used in mapping the input feature space in the SVM procedure. Figure 5 compares the performance of _Inc_Model_ and _Retrain_Model_ in terms of receiver operating characteristic (ROC) curves. The curves depict the trade-off between the TPR and FPR rates for TP1, TP2, and FP.  
Figure 4: TP2 Sensitivity Convergence Rate as a Function of _Inc_Set Sizes.  
Figure 5 indicates that as TPR increases, FPR increases as well because the FPR which makes _WP-SVM_ a good decision method will simultaneously have a reasonably high detection sensitivity and specificity for a specific setting of \(\zeta\). Since _WP-SVM_ reached a sensitivity of 91 % and 96 % for TP1 and TP2 with a specificity of 90.3% and 90 % and an average of 3.2 false positive per patient respectively. Since the area under the ROC curve of _WP-SVM_ is greater than the area under a hypothetical diagonal line which would represent a random guess, we can conclude that the obtained _WP-SVM_ ROC curves are informative and that _WP-SVM_ presents a promising online learning algorithm for detecting polyps.  
On average, detection performance reported by the CAD schemes used for binary classification in a non-dynamic scheme, as shown in Table 5, has varied between 50% and 100% with 1.5 to 15.7 false positives per patient. The _WP-SVM_ results for false-positive findings per patient compares favorably with these published results, especially when we consider that _WP-SVM_ is being applied as an online multi-classifier on a larger database. Note that mutli-classification accuracy is expected to be negatively impacted in comparison to binary classification. The parametric model of the SVM allows for adjustments when constructing the discriminant function. However, for multiclass problems these parameters do not always exhibit a perfect fit across the entire data set. This is partly supported by the fact that the VC dimension \"h\" impacts the generalization error and is bounded by the slope of the  
Figure 5: FP, TP2 and TP1 ROC Curves for _Retrain_Model_ and _Inc_Model_.  
\begin{table}
\begin{tabular}{l l l} \hline \hline Reference & Results & Settings \\ \hline
[33] & 95\%, average of 1.5 false positive per patient & 72 patients, 144 data sets, 21 polyps \(>\)\(\approx\)5 mm in 14 patients \\
[34] & 90.5\%, average of 2.4 false positive per patient & 121 patients, 242 data sets,  
hyperplane w and R the radius of the smallest sphere that contains all the training points according to [28] :  
\[h<\frac{R^{2}}{\left\|w\right\|^{2}}\]  
Finally, Table 6 compares the storage requirements of the _Retrain_Model vs._ the _Inc_model_ when _WP-SVM_ is applied. Over time, as the polyps' database increases, computer storage for the _Retrain_Model_ will require memory space proportional to the number of CTC acquired so that the model can be retrained each time a new CTC is acquired. For the _Inc_model_, the memory space is reduced to the number of features_f_ multiplied by the number of different classes.