### What is Super Vector Machine?

A supervised machine learning approach called Support Vector Machine (SVM) is used for regression as well as classification. Even yet, classification problems are the most appropriate use for regression problems. The SVM algorithm’s primary goal is to locate the best hyperplane in an N-dimensional space that may be used to divide data points into various feature space classes. The hyperplane attempts to maintain the largest possible buffer between the nearest points of various classes. The number of features determines the hyperplane’s dimension. The hyperplane is essentially a line if there are just two input features. The hyperplane transforms into a 2-D plane if there are three input features. It gets harder to envision when the number of features exceeds three.

**How does it woks?**

Support Vector Machines (SVM) are a powerful set of supervised learning algorithms used for classification and regression tasks. The main idea behind SVM is to find the best hyperplane that separates data points of different classes. Here’s a detailed explanation of how SVM works:

**Choosing the Best Hyperplane**

Given a set of data points belonging to two different classes, there can be multiple hyperplanes that can separate these classes. The goal is to choose the hyperplane that maximizes the margin, which is the distance between the hyperplane and the nearest data points from each class. This hyperplane is known as the maximum-margin hyperplane or hard margin.

**Handling Outliers**

In real-world scenarios, data often contains outliers. Consider a situation where an outlier exists within the boundary of another class. SVM handles this by finding the best hyperplane that maximizes the margin while ignoring the outlier. This results in a robust model that is less sensitive to outliers.

**Soft Margins**

When dealing with data that is not perfectly separable, SVM introduces the concept of soft margins. The algorithm aims to maximize the margin while allowing some points to cross the boundary, penalizing these violations. The objective is to minimize a combination of the margin and the sum of the penalties for points that cross the boundary. The hinge loss is a commonly used penalty function, where there is no penalty if there are no violations, and the penalty increases with the distance of the violation.

**Non-linearly Separable Data**

For data that is not linearly separable, SVM uses a technique called the kernel trick to map the original data into a higher-dimensional space where it becomes linearly separable.

Example: Mapping 1D Data to 2D

Consider a 1D dataset that is not linearly separable. SVM can create a new variable using a kernel function. For instance, if we have a point

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on a line, we can create a new variable

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y

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as a function of the distance from the origin. This transformation maps the data into a 2D space, making it easier to separate the classes with a linear hyperplane.

### Support Vector Machine Types

Two primary categories of Support Vector Machines (SVM) can be distinguished based on the type of decision boundary:

**Linear SVM:**To divide the data points into distinct classes, linear SVMs employ a linear decision boundary. Linear SVMs are ideal when the data can be precisely divided along a linear path. This indicates that the data points may be completely divided into their corresponding classes by a single straight line in two dimensions or a hyperplane in three dimensions. The decision boundary is a hyperplane that optimizes the margin between the classes.**Non-Linear SVM:**In situations where a straight line cannot divide data into two groups, non-linear SVM can be utilized to classify the data (in the case of 2D). Through kernel function utilization, nonlinear SVMs can manage data that is not linearly separable. These kernel functions convert the original input data into a higher-dimensional feature space in which the data points are linearly separable. In this modified space, a nonlinear decision boundary is found using a linear SVM.

## FAQ’s

**Q: What is the primary goal of the SVM algorithm?**

**A:** The primary goal of the Support Vector Machine (SVM) algorithm is to find the best hyperplane that separates data points of different classes in an N-dimensional space. This hyperplane maximizes the margin, which is the distance between the hyperplane and the nearest data points from each class, ensuring the best possible separation between the classes.

**Q: How does SVM handle outliers in the data?**

**A:** SVM handles outliers by finding the best hyperplane that maximizes the margin while ignoring the outliers. This approach results in a robust model that is less sensitive to outliers, ensuring that the overall classification or regression performance is not significantly affected by a few outlying data points.

**Q: What is the difference between linear and non-linear SVMs?**

**A:** Linear SVMs use a linear decision boundary to separate data points, which is ideal for data that can be separated by a straight line (in 2D) or a hyperplane (in higher dimensions). Non-linear SVMs, on the other hand, use kernel functions to map the original data into a higher-dimensional space where it becomes linearly separable. This allows non-linear SVMs to handle data that cannot be separated by a straight line or hyperplane in its original form.

**Q: What is the role of the kernel trick in SVM?**

**A:** The kernel trick in SVM is used to handle non-linearly separable data. It involves mapping the original input data into a higher-dimensional feature space using a kernel function, where the data points become linearly separable. In this transformed space, a linear SVM is applied to find the decision boundary, which is then used to classify the data in the original space. This allows SVM to effectively deal with complex data distributions.