Independent Principal Component Analysis for biologically meaningful dimension reduction of large biological data sets

Fangzhou Yao,Kim-Anh Lê Cao,Jeff Coquery

doi:10.1186/1471-2105-13-24

Abstract

BackgroundA key question when analyzing high throughput data is whether the information provided by the measured biological entities (gene, metabolite expression for example) is related to the experimental conditions, or, rather, to some interfering signals, such as experimental bias or artefacts. Visualization tools are therefore useful to better understand the underlying structure of the data in a 'blind' (unsupervised) way. A well-established technique to do so is Principal Component Analysis (PCA). PCA is particularly powerful if the biological question is related to the highest variance. Independent Component Analysis (ICA) has been proposed as an alternative to PCA as it optimizes an independence condition to give more meaningful components. However, neither PCA nor ICA can overcome both the high dimensionality and noisy characteristics of biological data.ResultsWe propose Independent Principal Component Analysis (IPCA) that combines the advantages of both PCA and ICA. It uses ICA as a denoising process of the loading vectors produced by PCA to better highlight the important biological entities and reveal insightful patterns in the data. The result is a better clustering of the biological samples on graphical representations. In addition, a sparse version is proposed that performs an internal variable selection to identify biologically relevant features (sIPCA).ConclusionsOn simulation studies and real data sets, we showed that IPCA offers a better visualization of the data than ICA and with a smaller number of components than PCA. Furthermore, a preliminary investigation of the list of genes selected with sIPCA demonstrate that the approach is well able to highlight relevant genes in the data with respect to the biological experiment.IPCA and sIPCA are both implemented in the R package mixomics dedicated to the analysis and exploration of high dimensional biological data sets, and on mixomics' web-interface.

Highlights

A key question when analyzing high throughput data is whether the information provided by the measured biological entities is related to the experimental conditions, or, rather, to some interfering signals, such as experimental bias or artefacts
Simulation study In order to understand the benefits of Independent Principal Component Analysis (IPCA) compared to Principal Component Analysis (PCA) or Independent Component Analysis (ICA), we simulated 5000 data sets of size n = 50 samples and p = 500 variables from a multivariate normal distribution with a pre-specified variance-covariance matrix described in the ‘Methods’ Section
We have developed a variant of PCA called IPCA that combines the advantages of both PCA and ICA

Summary

Introduction

A key question when analyzing high throughput data is whether the information provided by the measured biological entities (gene, metabolite expression for example) is related to the experimental conditions, or, rather, to some interfering signals, such as experimental bias or artefacts. Neither PCA nor ICA can overcome both the high dimensionality and noisy characteristics of biological data. Amongst the different categories of unsupervised approaches (clustering, model-based and projection methods), we are interested in projection-based methods, which linearly decompose the data into components with a desired property. These exploratory approaches project the data into a new subspace spanned by the components. They allow dimension reduction without loss of essential information and visualization of the data in a smaller subspace

Methods

Results

Conclusion