Book Image

A Handbook of Mathematical Models with Python

By : Dr. Ranja Sarkar
Book Image

A Handbook of Mathematical Models with Python

By: Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

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...