tukivektoriverkkojen

Tukivektoriverkkojen, often abbreviated as SVM, is a supervised machine learning algorithm used for classification and regression tasks. It is a powerful tool that works by finding the optimal hyperplane that best separates data points belonging to different classes. The goal of an SVM is to maximize the margin, which is the distance between the hyperplane and the closest data points from each class, known as support vectors.

In a classification setting, SVMs aim to find a decision boundary that maximizes this margin. For linearly separable data, this is a straightforward process. However, for non-linearly separable data, SVMs employ the "kernel trick." This technique implicitly maps the data into a higher-dimensional space where it may become linearly separable. Common kernels include the radial basis function (RBF) kernel, polynomial kernel, and linear kernel.

For regression problems, a variation called Support Vector Regression (SVR) is used. Instead of maximizing the margin between classes, SVR aims to find a hyperplane that best fits the data within a specified margin of tolerance, often denoted by epsilon ($\epsilon$). Data points within this margin do not contribute to the loss function.

SVMs are known for their effectiveness in high-dimensional spaces and when the number of dimensions is greater than the number of samples. They are also relatively memory efficient as they only use a subset of training points (support vectors) in the decision function. However, training time can be significant for very large datasets, and choosing the right kernel and parameters can be crucial for optimal performance.