Tukivektoreihin

Tukivektoreihin, often translated as support vectors, are a fundamental concept in the field of machine learning, particularly within Support Vector Machines (SVMs). In the context of classification, support vectors are the data points from the training set that lie closest to the decision boundary. This decision boundary is the hyperplane that optimally separates different classes of data.

The key characteristic of support vectors is their critical role in defining this boundary. If these points were removed, the position and orientation of the decision boundary would change. Conversely, points further away from the boundary, even if misclassified, do not influence the placement of the hyperplane. This makes SVMs robust to outliers that are far from the separating hyperplane.

The algorithm's name, Support Vector Machine, directly derives from the importance of these specific data points. During the training process, the SVM algorithm aims to find the hyperplane with the largest margin, which is the largest distance between the hyperplane and the nearest training data points of any class. The support vectors are precisely these nearest data points that lie on the edges of this margin.

The number of support vectors is often significantly smaller than the total number of training samples. This sparsity is a desirable property as it means the model's prediction depends only on a subset of the training data, making the model more efficient for classification and requiring less storage. The concept extends to regression tasks as well, where support vectors are points that lie within the margin of tolerance around the regression function.