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Misaligned Principal Component Analysis

A. Tibau-Puig, A. Wiesel, R.R. Nadakuditi and A. O. Hero

Abstract

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.

Papers

  • 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 Package

Matlab/Octave scripts implementing the experiments and data analysis presented in the above references can be found in the following GitHub repository:

https://github.com/atibaup/MisPCA

Or available as a zip file from MisPCA [zip]

Requirements:

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.

License

Copyright © 2011, Arnau Tibau-Puig and Alfred O. Hero III, University of Michigan All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  • Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  • Neither the name of the University of Michigan nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.