#### Overview of this book

The F# functional programming language enables developers to write simple code to solve complex problems. With F#, developers create consistent and predictable programs that are easier to test and reuse, simpler to parallelize, and are less prone to bugs. If you want to learn how to use F# to build machine learning systems, then this is the book you want. Starting with an introduction to the several categories on machine learning, you will quickly learn to implement time-tested, supervised learning algorithms. You will gradually move on to solving problems on predicting housing pricing using Regression Analysis. You will then learn to use Accord.NET to implement SVM techniques and clustering. You will also learn to build a recommender system for your e-commerce site from scratch. Finally, you will dive into advanced topics such as implementing neural network algorithms while performing sentiment analysis on your data.
F# for Machine Learning Essentials
Credits
Foreword
Acknowledgments
www.PacktPub.com
Preface
Free Chapter
Introduction to Machine Learning
Information Retrieval
Collaborative Filtering
Sentiment Analysis
Index

## QR decomposition of a matrix

The general linear regression model calculation requires us to find the inverse of the matrix, which can be computationally expensive for bigger matrices. A decomposition scheme, such as QR and SVD, helps in that regard.

QR decomposition breaks a given matrix into two different matrices—Q and R, such that when these two are multiplied, the original matrix is found.

In the preceding image, X is an n x p matrix with n rows and p columns, R is an upper diagonal matrix, and Q is an n x n matrix given by:

Here, Q1 is the first p columns of Q and Q2 is the last n – p columns of Q.

Using the Math.Net method QR you can find QR factorization:

Just to prove the fact that you will get the original matrix back, you can multiply Q and R to see if you get the original matrix back:

```let myMatAgain = qr.Q * qr.R
```

### SVD of a matrix

SVD stands for Single Value Decomposition. In this a matrix, X is represented by three matrices (the definition of SVD is taken from Wikipedia).

Suppose M...