Support Vector Machines (SVM) are powerful supervised learning models used for classification and regression. In this post, we’ll break down the geometry and logic behind them.
The Goal: Finding the Best Boundary
Imagine you have two groups of data points on a 2D graph. You want to draw a line that separates them. There are many lines you could draw, but which one is the “best”?
Hyperplanes 🔎
In SVM, the boundary that separates the data is called a Hyperplane. * In 2D, a hyperplane is a 1D line. * In 3D, a hyperplane is a 2D plane. * In N dimensions, a hyperplane has N-1 dimensions.
Margin and Support Vectors 🚂
SVM doesn’t just find any line; it finds the one with the Maximum Margin.
- Support Vectors: These are the data points from each class that are closest to the boundary. They “support” the hyperplane.
- Margin: The distance between the hyperplane and the support vectors.
The goal of SVM is to maximize this margin. A wider margin acts like a “safety buffer,” making the model more robust to new, slightly different data.
The Kernel Trick 🚂
What if the data isn’t linearly separable? Imagine a ring of “Type A” points surrounding a circle of “Type B” points. No straight line can separate them.
SVM solves this using the Kernel Trick. It mathematically transforms the data from a lower dimension to a higher dimension where a flat hyperplane can separate them.
Think of it like lifting the “Type B” points off the table into the air; now you can slide a sheet of paper (a plane) between them and the “Type A” points on the table.
Summary
- SVM looks for the widest possible “street” between classes.
- Support Vectors are the most important points that define that street.
- The Kernel Trick allows SVM to solve complex, non-linear problems.
Exercise
Research these terms to see the math behind SVM: 1. Lagrange Multipliers 2. Platt’s SMO Algorithm (The standard algorithm for training SVMs)
Next, we move into the world of Neural Networks—the foundation of modern AI.
Written by
Abdur-Rahmaan Janhangeer
Chef
Python author of 7+ years having worked for Python companies around the world
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