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What are Support Vector Machines?
Support Vector Machines (SVMs) are supervised machine learning models that are widely used for classification and regression tasks. SVMs are particularly effective in dealing with high-dimensional and complex datasets. The key idea behind SVMs is to find an optimal hyperplane that separates the data points of different classes with the maximum margin. The hyperplane is defined as the decision boundary that maximizes the distance between the closest data points of different classes, called support vectors. SVMs aim to achieve both good classification performance and robustness to new data.
Key aspects of Support Vector Machines are:
Linear and Nonlinear Classification: SVMs can perform linear classification by finding a hyperplane that separates the data points. They can also handle nonlinear classification by using kernel functions that map the data into a higher-dimensional feature space, where a linear decision boundary can be found.
Margin Maximization: SVMs seek to maximize the margin, which is the distance between the decision boundary and the support vectors. By maximizing the margin, SVMs promote generalization and help avoid overfitting, leading to better classification performance on new, unseen data.
Kernel Functions: Kernel functions allow SVMs to efficiently operate in high-dimensional feature spaces. They implicitly map the data to a higher-dimensional space, avoiding the need to explicitly compute the transformations. Popular kernel functions include linear, polynomial, radial basis function (RBF), and sigmoid kernels.
C-parameter and Soft Margin: SVMs introduce a regularization parameter, C, which controls the trade-off between the margin width and the training errors. A smaller C allows more errors but wider margins, while a larger C reduces the margin but allows fewer errors. This parameter helps balance model complexity and generalization.
Support Vector Regression: In addition to classification, SVMs can also be used for regression tasks. Support Vector Regression (SVR) aims to find a regression function that lies within a specified margin of the training data points. It seeks to fit the data while limiting the deviation from the true function.
Support Vector Machines have several advantages, including their ability to handle high-dimensional data, resilience to overfitting, and effective handling of nonlinear relationships. However, SVMs can be sensitive to the choice of parameters and can be computationally expensive for large datasets. To use SVMs effectively, it is important to carefully select the appropriate kernel function and tune the hyperparameters, such as the C-parameter and kernel parameters. Additionally, preprocessing the data and addressing class imbalances can also impact the performance of SVM models.
Support Vector Machines are covered in more detail in module 4 of the CQF program.