Support vectors are key elements in Supprot Vector Machines, a popular supervised learning algorithm used for classification and regression tasks.
Support vectors are data points that lie closest to the decision boundary (hyperplane) and play a crucial role in defining that boundary. These points help maximize the margin, which is the distance between the separating hyperplane and the nearest data points from each class.
Role of Support Vectors in SVM
- They determine the optimal hyperplane that maximizes the margin between different classes.
- Only support vectors influence the decision boundary, making SVMs efficient, especially in high-dimensional spaces.
- If the support vectors are removed or changed, the decision boundary may shift, showing their importance in classification.
Importance of Support Vectors
- Robustness: Since only a few support vectors determine the decision boundary, SVMs are less affected by outliers outside this boundary.
- Generalization: A large margin (maximized by support vectors) helps improve the model’s generalization ability.
- Flexibility: With the kernel trick, SVMs can map data into higher dimensions where a linear boundary becomes possible, allowing support vectors to define complex decision boundaries.
Support Vectors in Soft-Margin and Hard-Margin SVM
- Hard-Margin SVM: Used when data is perfectly separable; support vectors lie exactly on the margin.
- Soft-Margin SVM: Used for non-linearly separable data, allowing some misclassification while still maximizing the margin.
Reference: Some of the text in this article has been generated using AI tools such as ChatGPT and edited for content and accuracy.
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