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A Handbook of Mathematical Models with Python

You're reading from   A Handbook of Mathematical Models with Python Elevate your machine learning projects with NetworkX, PuLP, and linalg

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Product type Paperback
Published in Aug 2023
Publisher Packt
ISBN-13 9781804616703
Length 144 pages
Edition 1st Edition
Languages
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Author (1):
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Ranja Sarkar Ranja Sarkar
Author Profile Icon Ranja Sarkar
Ranja Sarkar
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Table of Contents (16) Chapters Close

Preface 1. Part 1:Mathematical Modeling
2. Chapter 1: Introduction to Mathematical Modeling FREE CHAPTER 3. Chapter 2: Machine Learning vis-à-vis Mathematical Modeling 4. Part 2:Mathematical Tools
5. Chapter 3: Principal Component Analysis 6. Chapter 4: Gradient Descent 7. Chapter 5: Support Vector Machine 8. Chapter 6: Graph Theory 9. Chapter 7: Kalman Filter 10. Chapter 8: Markov Chain 11. Part 3:Mathematical Optimization
12. Chapter 9: Exploring Optimization Techniques 13. Chapter 10: Optimization Techniques for Machine Learning 14. Index 15. Other Books You May Enjoy

Support vectors in SVM

SVM is an algorithm that can produce significantly accurate results with less computation power. It is widely used in data classification tasks. If a dataset has n number of features, SVM finds a hyperplane in the n-dimensional space, which is also called the decision boundary, to classify the data points. An optimal decision boundary maximizes the distance between the boundary and instances in both classes. The distance between data points in the classes (shown in Figure 5.1a) is known as the margin:

Figure 5.1a: Optimal hyperplane

Figure 5.1a: Optimal hyperplane

An SVM algorithm finds the optimal line in two dimensions or the optimal hyperplane in more than two dimensions that separates the space into classes. The optimal hyperplane or optimal line maximizes the margin (the distance between the data points of the two classes). In 3D (or more), data points become vectors and those (very small subset of training examples) that are closest to or on the hyperplanes...

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