Elegant SciPy

Chapter 2. Quantile Normalization with NumPy and SciPy

Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you.

Edwin A. Abbott, Flatland: A Romance of Many Dimensions

In this chapter, we will continue to analyze the gene expression data from Chapter 1, but with a slightly different purpose: we want to use each patient’s gene expression profile (the full vector of their gene expression measurements) to predict their expected survival. In order to use full profiles, we need a stronger normalization than what Chapter 1’s RPKM provides. We will instead perform quantile normalization, a technique that ensures measurements fit a specific distribution. This method enforces a strong assumption: if the data are not distributed according to a desired shape, we just make it fit! This might feel a bit like cheating, but it turns out to be simple and useful in many cases where the specific distribution doesn’t matter, but the relative changes of values within a population are important. For example, Bolstad and colleagues showed that it performs admirably in recovering known expression levels in microarray data.

Over the course of the chapter, we will reproduce a simplified version of Figures 5A and 5B from “Genomic Classification of Cutaneous Melanoma,” a paper from The Cancer Genome Atlas (TCGA) project.

Our implementation of quantile normalization uses NumPy and SciPy effectively to produce a function that is fast, ...