# An Agent-Ensemble for Thresholded Multi-Target Classification
## 5 Experiments
### Pin-Less Verification with Yale Faces  
We perform a pin-less biometric verification experiment using the cropped version of the Extended Yale Faces dataset [28]. The dataset contains frontal images of thirty-nine people, with sixty-five images of each person taken under different lighting conditions. In order to perform the pin-less verification experiment, we make persons one through five the targets, referred to as clients within the biometrics literature, and the remaining users the clutter, referred to as impostors. The original images are 192 x 168 pixels. We down sample the images by a factor of two (The Yale Faces data is often down sampled in order to improve computational efficiency [29; 30]), vectorize the resulting pixels, and perform principal components analysis retaining components that contain 95% of the data variance. This results in a sixty-four dimensional feature vector for each image. We randomly select \(n\) images from each person in the client group for training and use the rest for testing. We randomly select twenty persons from the impostor group and use all of their images for training while using all images from the remaining fourteen impostors for testing. We vary the number of training images for each client over the set \(n\in\{5,10,20,30,40\}\). We repeat the experiment twenty-five times for each \(n\), randomly selecting different training and test images for each iteration. We train five SVM agents, with the training data for the \(i^{\text{th}}\) agent consisting of the \(n\) images for client \(i\) as target and all images from the twenty training impostors as clutter. We choose the SVM parameters via cross-validation on the training data, and then get unbiased training data for training the combiners by cross-validation. We compare the combiner strategies from the previous section along with the addition of the proposed combiner with weighted likelihood normalization estimated via the Platt probabilistic normalization as described in Section 4.4 (_Prpsd. Platt WLR_) and a meta-SVM classifier using the \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(\mathbf{\alpha=0.95}\) & \(\mathbf{\alpha=0.8}\) & \(\mathbf{\alpha=0.6}\) & \(\mathbf{\alpha=0.4}\) & \(\mathbf{\alpha=0.1}\) \\ \hline Prpsd. Gaussian WLR & **0.464** & **0.473** & **0.476** & **0.500** & 0.508 \\ Joint Gaussian & 0.371 & 0.383 & 0.402 & 0.432 & 0.483 \\ Ind. Gaussian & 0.418 & 0.440 & 0.463 & **0.497** & **0.538** \\ AC Gaussian WLR & 0.457 & 0.463 & 0.461 & 0.480 & 0.487 \\ AC Z-norm & **0.461** & 0.466 & **0.474** & 0.490 & 0.503 \\ AC F-norm & 0.452 & 0.460 & 0.471 & 0.483 & 0.490 \\ AC EER-norm & **0.464** & 0.468 & **0.478** & 0.491 & 0.510 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average PAUC for simulation two with 100 combiner training samples. Boldface identifies results that are the best or statistically significantly tied for the best with 95% confidence. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \(\mathbf{\alpha=0.95}\) & \(\mathbf{\alpha=0.8}\) & \(\mathbf{\alpha=0.6}\) & \(\mathbf{\alpha=0.4}\) & \(\mathbf{\alpha=0.1}\) \\ \hline Prpsd. Gaussian WLR & **0.479** & **0.492** & 0.504 & 0.521 & 0.543 \\ Joint Gaussian & 0.469 & 0.489 & **0.506** & **0.535** & 0.584 \\ Ind. Gaussian & 0.444 & 0.467 & 0.496 & 0.534 & **0.589** \\ AC Gaussian WLR & 0.471 & 0.482 & 0.490 & 0.504 & 0.521 \\ AC Z-norm & 0.471 & 0.483 & 0.491 & 0.505 & 0.522 \\ AC F-norm & 0.469 & 0.481 & 0.490 & 0.503 & 0.522 \\ AC EER-norm & 0.465 & 0.474 & 0.481 & 0.492 & 0.510 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average PAUC for simulation two with 1000 combiner training samples. Boldface identifies results that are the best or statistically significantly tied for the best with 95% confidence. Gaussian RBF kernel (_Meta SVM_). We choose parameters for the meta-SVM via cross-validation on the combiner training data from the same pool of parameters used to train the agent classifiers. Table 4 gives the results.