A support vector machine (SVM) is a powerful machine learning algorithm used for classification and regression tasks. In the context of classification, SVMs are particularly effective at separating data points into different classes by constructing hyperplanes in a high-dimensional feature space. When it comes to classifying unknown data points, SVMs employ a decision boundary that is learned during the training phase.
To understand how SVMs classify unknown data points, it is important to first grasp the concept of the decision boundary. The decision boundary is a hypersurface that separates the feature space into different regions, each corresponding to a specific class. In a binary classification scenario, the decision boundary is essentially a line or a hyperplane that separates the two classes. The goal of SVMs is to find the decision boundary that maximizes the margin between the classes.
During the training phase, SVMs identify a subset of training examples called support vectors. These support vectors are the data points that lie closest to the decision boundary. They play a important role in defining the decision boundary and ultimately determining the classification of unknown data points.
Once the decision boundary is learned, SVMs can classify unknown data points by determining which side of the decision boundary they fall on. If a data point lies on one side of the decision boundary, it is classified as belonging to one class, and if it lies on the other side, it is classified as belonging to the other class.
The classification process involves computing the distance between the unknown data point and the decision boundary. This distance is typically measured as the perpendicular distance from the data point to the decision boundary. If the distance is positive, the data point lies on one side of the decision boundary and is classified accordingly. If the distance is negative, the data point lies on the other side of the decision boundary and is classified accordingly. The magnitude of the distance can also provide additional information about the confidence of the classification.
To summarize, SVMs classify unknown data points by determining which side of the decision boundary they fall on. The decision boundary is learned during the training phase and is defined by a subset of training examples called support vectors. By computing the distance between the unknown data point and the decision boundary, SVMs can assign the data point to a specific class.
In practice, the classification process of SVMs can be visualized using a simple example. Consider a binary classification problem where we want to separate data points belonging to two classes, represented by red and blue points. The decision boundary learned by the SVM is a line that separates the two classes, as shown in the following figure:
![SVM Decision Boundary](https://example.com/svm_decision_boundary.png)
In this example, the decision boundary is a line, and the support vectors are the data points lying closest to the decision boundary. The unknown data point (marked with a question mark) can be classified by computing its distance to the decision boundary. If the distance is positive, the data point is classified as belonging to the red class. If the distance is negative, the data point is classified as belonging to the blue class.
SVMs classify unknown data points by determining which side of the decision boundary they fall on. This is achieved by computing the distance between the data point and the decision boundary. SVMs are powerful classifiers that can handle complex decision boundaries and are widely used in various machine learning applications.
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