Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Chapter 12: Principal Component Analysis with Scikit-Learn

In this chapter, we will learn about principal component analysis (PCA), which is a core machine learning technique that reduces the dimensionality of large datasets to determine which variables can best explain strong patterns in data. We will first introduce some mathematical concepts about orthogonal matrices and bases. Then, we will explain the method and look at the scikit-learn library's implementation of PCA. Lastly, we will apply PCA to some real-world data.

In this chapter, we will cover the following topics:

  • Understanding eigenvalues, eigenvectors, and orthogonal bases
  • The principal component analysis approach to dimensionality reduction
  • The scikit-learn implementation of PCA
  • An application of PCA to real-world data

By the end of this chapter, you will have learned the intuition and mathematics behind PCA. You will also learn about the scikit-learn library's implementation...