Final answer:
The output of SVM training is support vectors and their corresponding weights, which are used to determine the optimal hyperplane for classifying new examples in tasks like classification and regression.
Step-by-step explanation:
The output of the SVM (Support Vector Machine) training process is a set of support vectors and the corresponding weights. SVM is a supervised machine learning algorithm widely used for classification and regression tasks. The support vectors are the data points that lie closest to the decision boundary, determined during the training process. These points are critical as they define the position and orientation of the decision boundary. The weights, along with the support vectors, are used to create the optimal hyperplane that separates different classes.
During the classification process, SVM uses these parameters to classify new examples. The strength and direction of the influence of each support vector are determined by its associated weight. A positive weight reflects one class, while a negative weight reflects the other. Hence, when a new data point is introduced, the SVM categorizes it based on the learned decision function, which involves the support vectors and their weights.
Example:
Consider a set of data points belonging to two different classes plotted on a two-dimensional space. In the case of a linear SVM, the algorithm will find the line (hyperplane in higher dimensions) that maximizes the margin between the two classes. The support vectors would be the closest points to this line from both classes, and their weights signify their importance in determining the position of the line.