Misaligned Principal Component Analysis
A. Tibau-Puig, A. Wiesel, R.R. Nadakuditi and A. O. Hero
Principal Component Analysis (PCA) is a widely applied method for extracting structure from samples of high dimensional biological data. Often there exist misalignments between different samples and this can cause severe problems in PCA if not properly taken into account. For example, subject-dependent temporal differences in gene expression response to a treatment will create relative time shifts in the samples that decohere the PCA analysis. Depending on the characteristics of the underlying signal, the sensitivity of PCA to such misalignments is severe, leading to a phase transition phenomenon that can be studied using the spectral theory of autocorrelation matrices. With this as motivation, we propose a new method of PCA, called MisPCA, that explicitly accounts for the effects of misalignments in the samples. We illustrate MisPCA on clustering longitudinal temporal gene expression data.
Tibau-Puig, A., Wiesel, A., R.R. Nadakuditi and Hero, A.O. , “Misaligned Principal Component Analysis (Mis-PCA) for Gene Expression Time Series Analysis” (preprint)
Tibau-Puig, A., “PhD Thesis, Chapter 5” (preprint)
Matlab/Octave scripts implementing the experiments and data analysis presented in the above references can be found in the following GitHub repository:
Or available as a zip file from MisPCA [zip]
The code has been tested on GNU Octave Version 3.2.4 with the following packages:
Package | Version
control | 1.0.11 |
miscellaneous | 1.0.11 |
optim | 1.0.17 |
signal | 1.0.11 |
specfun | 1.0.9 |
struct | 1.0.9 |
Comments and remarks
This is package is constantly under development. If you find any bugs or errors, you may report them to the first author of the paper.
Copyright © 2011, Arnau Tibau-Puig and Alfred O. Hero III, University of Michigan All rights reserved.
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