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Finally, if no satisfactory kernel can be found, the constraint that all training examples are correctly classified can be relaxed (soft-margin SVM).

This guarantees that all examples are correctly classified, and that the examples that lie closest to the separating hyperplane are as far as possible from the latter; in other words, the margin of the classifier, i.e., the distance between the separating surface and the examples is as large as possible (Figure 8). Figure 8 Optimal separating hyperplane for linearly separable examples.

The disparate trends in the two groups of gene pairs sets do not prove that all training set examples are correctly labeled or that all gene pairs can be discretely labeled but it does indicate that the genes labeled redundant, in general, show distinct attributes from those labeled non-redundant.

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All the training examples were correctly identified by the algorithm, suggesting the possibility of overfitting.

Table 1 Confusion matrix of a classifier [37]   Classified positive Classified negative Actual positive TP FN Actual negative FP TN In Table 1, TP and TN indicate the numbers of positive examples and negative examples that are correctly classified, respectively; FN and FP indicate the numbers of positive examples and negative examples that are incorrectly classified, respectively.

Of these novel positive examples, 339 non-coding examples (85%) and 1955 coding examples (89%) are correctly predicted by our classifier at the default threshold.

The first three rows illustrate natural image context examples that are correctly grasped by aspect model 2. The fourth row shows a correctly estimated man-made context that leads to an improved classification of patches for aspect model 2. In the fifth example, however, the overestimation of the man-made related aspects leads to patches that are dominantly classified as man-made.

The performance of each classifier is presented as the percentage of test set examples which are correctly classified.

The trade-off for this higher PPV is a decrease in the sensitivity, i.e., the percentage of positive examples that are correctly identified.

The tuning selects the value of Δ that maximizes TP + TN, with TP the true positive rate and TN the proportion of negative examples that are correctly classified.

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