Støttevektorer

Støttevektorer, also known as support vectors, are a fundamental concept in the field of machine learning, particularly in the context of support vector machines (SVMs). They are the data points that lie closest to the decision boundary or hyperplane that separates different classes in a dataset. These points are crucial because they define the position and orientation of the hyperplane, and thus, the classification boundary.

In a binary classification problem, the goal of an SVM is to find the hyperplane that maximizes the margin between the two classes. The margin is defined as the distance between the hyperplane and the nearest data points from either class. These nearest data points are the support vectors. They are "supporting" the hyperplane because if these points were moved or removed, the position of the hyperplane would change.

Support vectors play a significant role in the training process of an SVM. The algorithm aims to maximize the margin, which is equivalent to minimizing the classification error on the training data. This is achieved by solving a quadratic optimization problem that involves the support vectors. Once the support vectors are identified, the hyperplane can be determined, and the SVM can be used to classify new, unseen data points.

The concept of support vectors can be extended to non-linear classification problems through the use of kernel functions. These functions transform the original feature space into a higher-dimensional space where a linear separation is possible. In this higher-dimensional space, the support vectors are the points that lie closest to the separating hyperplane.

In summary, støttevektorer are essential components in the construction of support vector machines. They are the data points that define the decision boundary and play a critical role in the training process of an SVM. Understanding the concept of support vectors is key to grasping the principles behind SVMs and their applications in various machine learning tasks.