What are the two methodologies for classifying multiple groups using support vector machines (SVM)? How do they differ in their approach?
The two methodologies for classifying multiple groups using support vector machines (SVM) are one-vs-one (OvO) and one-vs-rest (OvR). These methodologies differ in their approach to handling multi-class classification problems.
In the OvO approach, a separate binary SVM classifier is trained for each pair of classes. For N classes, this results in N * (N – 1) / 2 classifiers. During training, each classifier is trained on a subset of the data containing only the samples from the two classes it aims to distinguish. When making predictions, each classifier produces a binary decision for its corresponding pair of classes. The class that receives the most "votes" is then assigned as the predicted class. In this approach, the final decision is based on the combination of the binary decisions made by all the classifiers.
For example, suppose we have three classes: A, B, and C. With the OvO approach, we would train three binary SVM classifiers: one for A vs. B, one for A vs. C, and one for B vs. C. When making a prediction, each classifier would produce a binary decision: A vs. B (A), A vs. C (C), and B vs. C (B). The class that receives the most votes (A) would be assigned as the predicted class.
On the other hand, the OvR approach trains a single binary SVM classifier for each class, treating it as the positive class and the rest of the classes as the negative class. During training, each classifier is trained on a subset of the data where the positive class is the class it represents, and the negative class includes all the other classes. When making predictions, each classifier produces a binary decision: positive (the represented class) or negative (all other classes). The class associated with the classifier that produces the positive decision is then assigned as the predicted class.
Continuing with the previous example, with the OvR approach, we would train three binary SVM classifiers: one for A vs. rest, one for B vs. rest, and one for C vs. rest. When making a prediction, each classifier would produce a binary decision: A vs. rest (positive), B vs. rest (negative), and C vs. rest (negative). The class associated with the positive decision (A) would be assigned as the predicted class.
OvO trains multiple binary SVM classifiers for each pair of classes and combines their decisions to make the final prediction. OvR trains multiple binary SVM classifiers, each representing one class against the rest, and assigns the predicted class based on the positive decision made by one of the classifiers.
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