WBJECA 2025 — Computer PYQ

Support Vector Machines (SVMs) aim to find the optimal hyperplane that separates data points of different classes. The "margin" is a core concept in SVM optimization.

• Decision Boundary: The hyperplane that separates the classes.

• Support Vectors: These are the data points closest to the hyperplane. They are the "critical" points that define the position and orientation of the decision boundary.

• Margin: The margin is the width of the empty space between the decision boundary and the nearest data points (the support vectors) of each class. SVMs are designed to maximize this margin.

Mathematically, if the hyperplane is defined by $w^{T}x+b=0$, the distance from a point $x_i$ to the hyperplane is $\frac{|w^T{x}_i+b|}{||w||}$. For support vectors, where $w^T{x}_i+b=\pm 1$, the margin distance is:

$$\text{Margin Distance}=\frac{1}{||w||}$$

The total margin width, which SVM seeks to maximize, is defined as the distance between the support vectors of the two classes:

$$\text{Total Margin}=\frac{2}{||w||}$$

Since the margin is defined by the separation between the decision boundary and the support vectors that are closest to it, option (A) is the correct definition