Introduction to Support Vector Machines (SVMs)
Support Vector Machines (SVM) is a supervised machine learning algorithm introduced by Vladimir N. Vapnik and his colleagues in the 1990s. It excels in classification tasks by identifying an optimal hyperplane that maximizes the margin between classes, ensuring robust performance on unseen data. Leveraging the kernel trick, SVM can handle both linear and nonlinear classification, using various kernel functions like linear, polynomial, radial basis function (RBF), and sigmoid to adapt to diverse data patterns. After reading this article, you should know the following:
- What are SVMs?
- Linear SVM vs Nonlinear SVM Classification
- SVM Regression
- Uses for SVM
- Summary
What are Support Vector Machines?
Support Vector Machines (SVMs) is a supervised machine learning algorithm that works by finding an optimal decision boundary, or hyperplane, that separates different classes of data. It aims to maximize the margin between the closest data points from each class, called support vectors, and the hyperplane, which helps improve the model’s ability to generalize to new data. The algorithm uses optimization techniques to find the best hyperplane that maximizes the margin, making it effective for various complex classification tasks (Figure 1).
SVM algorithms work incredibly well when attempting to identify the largest possible separation hyperplane between the many classes present in the target feature.
Linear SVM vs Nonlinear SVM Classification
Main types of SVM based on the margin it employs for classification: linear SVM (including soft margin SVM) and nonlinear SVM.
Linear SVM:
- In linear SVM, the algorithm aims to find the hyperplane that best separates the classes in the feature space.
- The hyperplane is a decision boundary that maximizes the margin, which is the distance between the hyperplane and the nearest data points (support vectors) from each class.
- When the data is linearly separable, meaning classes can be separated by a straight line or plane in the feature space, then linear SVM works well.
- In cases where the data is not perfectly separable, linear SVM may still be used with a soft margin.
Soft Margin SVM vs Hard Margin SVM:
Hard Margin SVM: Hard Margin SVM aims to find the hyperplane that perfectly separates the classes in the training data without allowing any misclassifications. This means that it requires the data to be linearly separable and does not tolerate any outliers or noise in the dataset. If the data is not linearly separable, the optimization problem for Hard Margin SVM becomes infeasible and it fails to find a solution.
Soft Margin SVM: Soft Margin SVM, on the other hand, allows for some misclassification errors in the training set by introducing a regularization parameter (C). This parameter controls the trade-off between maximizing the margin and minimizing the classification error. A smaller value of C allows for a wider margin but may lead to more misclassifications, while a larger value of C penalizes misclassifications more heavily, potentially resulting in a narrower margin.
Nonlinear SVM:
Nonlinear Support Vector Machines (SVM) are used when input features and target classes do not follow a linear pattern. By using the kernel trick, nonlinear SVM transforms data into a higher-dimensional space where classes can be separated linearly. This allows the model to capture complex decision boundaries and handle nonlinear relationships. Techniques like polynomial and similarity features further enhance the model by adding interactions between features or measuring data point similarities, improving the model’s ability to identify intricate patterns. Popular kernels such as polynomial, radial basis function (RBF), and sigmoid kernels help optimize performance for diverse tasks (Figure 2).
1. Nonlinear SVM with Adding Polynomial Features:
- Generates new features by raising existing ones to various powers.
- Expands the feature space, allowing the model to capture non-linear relationships.
- May lead to overfitting with a high-dimensional feature space.
2. Nonlinear SVM with Polynomial Kernel:
- Utilizes polynomial functions to transform input features into a higher-dimensional space.
- Captures complex relationships between features and classes, introducing non-linearity.
- Requires careful selection of hyperparameters to prevent overfitting in (Figure 3).
3. Nonlinear SVM with Similarity Features:
- Transforms data into a higher-dimensional space using a similarity measure.
- Measures similarity between data points, capturing complex patterns.
- Particularly useful for modeling non-linear relationships in the data.
4. Nonlinear SVM with Gaussian RBF Kernel:
- Maps input features into an infinite-dimensional space using a Gaussian function.
- Measures similarity between data points, effectively capturing non-linear relationships.
- It provides flexibility in modeling complex data patterns but may be sensitive to hyperparameters in ( Figure 4)
SVM Regression
The SVM algorithm is very flexible, as we have already discussed. It enables both linear and nonlinear regression in addition to linear and nonlinear classification.
In SVM regression, the objective is to fit as many data points as possible within a margin (the “street”) while limiting violations, rather than maximizing the margin between classes like in classification.
The margin width is controlled by a hyperparameter, ϵ (epsilon), with larger values allowing a wider margin and smaller values creating a narrower one (Figure 5).
Uses for SVM
SVM has been used in many real-world regression and classification problems. The following list includes a few of the basic uses for SVM.
- Sorting text and hypertext
- Image categorization
- classification of synthetic-aperture radar (SAR) satellite data
- categorizing biological materials, such as proteins
Summary
Support Vector Machines (SVM) are versatile supervised learning models used for classification and regression tasks. They aim to find the optimal hyperplane that separates data into different classes while maximizing the margin. SVM is effective in high-dimensional spaces and can handle both linear and nonlinear relationships between features and classes. It employs the kernel trick to map data into higher-dimensional spaces, enabling it to capture complex decision boundaries. SVM is robust to overfitting and is widely used in various domains such as text classification, image recognition, and bioinformatics. Its versatility, robustness, and ability to handle nonlinear relationships make it a popular choice in machine learning applications.
