Support Vector Machines
151
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If
M·1
M·l
3
2
Fig. SA. The directed acyclic graph SVM (DAGSVM)
tree. The question is how to determine its structure. Use of Euclidean distance
or the Mahalanobis distance as a criterion has been proposed to determine
the decision tree structure. The top node is the most important classifier. The
better the classifier at the higher node, the better will be the overall classification
accuracy. Therefore, the higher nodes are designed to classify a class or some
classes that has/have the farthest distance from the remaining classes.
The input vector x is evaluated starting from the top of the decision tree.
The sign of the value of the decision function determines the path of the input
vector. The process is repeated until a leaf node is reached. The class label
corresponding to the final leaf node is associated with the input vector. It
clearly shows that the number of binary classifiers for this method is less than
the other aforementioned methods since the input is evaluated at most M - 1
times. However, it is important to mention that the construction of the decision
tree is critical to the overall classification performance.