Non-negative Matrix Factorization (NMF)

Preface

Some measurements are made of many numbers that are not, underneath, many independent pieces of information. Thousands of genes rise and fall together in a handful of shared programs. A tissue sample’s molecular profile is a mixture of a small number of underlying sources. A patient’s clinical picture is often a combination of a few recurring patterns, expressed in different amounts in different people.

Non-negative matrix factorization, NMF, is a method for finding that smaller set of patterns directly from the data, under one restriction that turns out to matter a great deal: every pattern, and every amount of every pattern, must be non-negative. Where that restriction fits the data, NMF tends to return components that read like ingredients or parts, present in some amount or absent.

To follow the course, you should be comfortable with basic matrix algebra and have seen PCA before, though the chapters do not assume you remember every detail of it.

Start with NMF.