KI-Glossar
Das vollständige Wörterbuch der Künstlichen Intelligenz
Optimal hyperplane
Decision boundary in a high-dimensional space that maximizes the distance between the closest classes, thus ensuring the best possible separation of data.
Support vector
Training points located on the margins that define the optimal hyperplane, these critical points determine the position and orientation of the decision boundary.
Maximum margin
Distance between the decision hyperplane and the closest training points of each class, which the SVM algorithm seeks to maximize to improve generalization.
Kernel function
Mathematical function that implicitly transforms data into a higher-dimensional space without performing the explicit transformation, allowing linear separation of non-linear data.
Linear SVM
Variant of SVM that uses a linear hyperplane to separate classes, particularly effective when data are linearly separable in their original space.
Non-linear SVM
Extension of SVM that uses kernel functions to project data into a higher-dimensional space where they become linearly separable.
Slack variable
Relaxation variables that allow some points to violate margin constraints, making the model more robust to noisy or non-separable data.
Hyperparameter C
Regularization parameter that controls the trade-off between margin maximization and classification error minimization, determining the penalty for margin violations.
One-Class SVM
Variant of SVMs used for anomaly detection where the algorithm learns a boundary around normal data to identify atypical observations.
SVR (Support Vector Regression)
Adaptation of SVMs for regression problems that seeks to find a function that deviates by at most an epsilon value from the targets while being as flat as possible.
Dual Formulation
Alternative mathematical representation of the SVM optimization problem that depends only on scalar products between observations, facilitating the use of kernel functions.
Feature Space
Transformed high-dimensional space where data can be linearly separated, obtained by applying the kernel function to the original data.
Multi-class SVM
Extension of binary SVMs to handle multi-class classification problems, typically implemented by one-against-one or one-against-all strategies.
RBF Kernel
Gaussian radial basis function kernel that maps data into an infinite-dimensional space, one of the most popular kernel functions for non-linear SVMs.
SMO (Sequential Minimal Optimization)
Efficient optimization algorithm to solve the dual problem of SVMs by iteratively optimizing Lagrange multipliers in pairs, reducing computational complexity.
Polynomial Kernel
Kernel function that computes the dot product of vectors in a polynomial feature space, allowing to capture higher-order non-linear relationships.
Soft margin
Extension of SVMs that allows certain margin constraint violations through slack variables, making the model more flexible to noisy or overlapping data.
Gamma (γ)
Hyperparameter of RBF and polynomial kernel functions that controls the influence of a single training example, determining the flexibility of the decision boundary.