# Classification

Classification is the final and the most essential part for CAD systems. In this section, we introduce some basic classifiers applied for positive staining pattern classification.

## Support Vector Machine

SVM classifier is one of the latest and most successful supervised learning classifiers and has been widely applied for image classification due to its efficiency. Using training labeled samples, a statistical model is constructed and then new samples can be classified according to this trained model. The linear SVM aims at searching for an optimal hyperplane (or hyperplanes) in feature space with a large separating margin and a minimal misclassiflcation rate.

For a binary linear SVM classifier, given training data and its corresponding labels *(x _{i}, yi), i = 1,2,...,l, Xi e R^{n}, y_{i}* e {-1, +1}, the concrete formulation can be defined by

where *C >* 0 is a penalty parameter to allow some misclassification and ? are slack variables. The objective function aims to maximize the margin and the constraints indicate that the training points should be correctly classified by the relaxed decision function w^{T}x + b. To extend binary SVM for multi-class problems, we use the *one- vs-all* approach [47]. We train a single binary SVM classifier per class by treating the cell images of this class as positive samples and those of other classes as negative samples. When classification is performed, all the binary classifiers are run and the classifier with the highest confidence score is chosen.