Book Image

Machine Learning with Swift

By : Jojo Moolayil, Alexander Sosnovshchenko, Oleksandr Baiev
Book Image

Machine Learning with Swift

By: Jojo Moolayil, Alexander Sosnovshchenko, Oleksandr Baiev

Overview of this book

Machine learning as a field promises to bring increased intelligence to the software by helping us learn and analyse information efficiently and discover certain patterns that humans cannot. This book will be your guide as you embark on an exciting journey in machine learning using the popular Swift language. We’ll start with machine learning basics in the first part of the book to develop a lasting intuition about fundamental machine learning concepts. We explore various supervised and unsupervised statistical learning techniques and how to implement them in Swift, while the third section walks you through deep learning techniques with the help of typical real-world cases. In the last section, we will dive into some hard core topics such as model compression, GPU acceleration and provide some recommendations to avoid common mistakes during machine learning application development. By the end of the book, you'll be able to develop intelligent applications written in Swift that can learn for themselves.
Table of Contents (18 chapters)
Title Page
Packt Upsell

Reasoning in high-dimensional spaces

Working with feature spaces of high dimensions requires special mental precautions, since our intuition used to deal with three-dimensional space starts to fail. For example, let's look at one peculiar property of n-dimensional spaces, known as an n-ball volume problem. N-ball is just a ball in n-dimensional Euclidean space. If we plot the volume of such n-ball (y axis) as a function of a number of dimensions (x axis), we'll see the following graph:

Figure 3.9: Volume of n-ball in n-dimensional space

Note that at the beginning the volume rises, until it reaches its peak in five-dimensional space, and then starts decreasing. What does it mean for our models? Specifically, for KNN, it means that starting from five features, the more features you have the greater should be the radius of the sphere centered on the point you're trying to classify to cover KNN.

The counter-intuitive phenomena that arise in a high-dimensional space are colloquially known as the...