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
Contributors
Preface
Index

Calculating the distance


How do we calculate a distance? Well, that depends on the kind of problem. In two-dimensional space, we used to calculate the distance between two points, (x1, y1) and (x2, y2), as 

—the Euclidean distance. But this is not how taxi drivers calculate distance because in the city you can't cut corners and go straight to your goal. So, they use (knowing it or not) another distance metric: Manhattan distance or taxicab distance, also known as l1-norm:

. This is the distance if we're only allowed to move along coordinate axes:

Figure 3.1: The blue line represents the Euclidean distance, the red line represents the Manhattan distance. Map of Manhattan by OpenStreetMap

Jewish German mathematician Hermann Minkowski proposed a generalization of both Euclidean and Manhattan distances. Here is the formula for the Minkowski distance:

where p and q are n-dimensional vectors (or coordinates of points in n-dimensional space if you wish). But what does c stand for? It is an order of...