Consensus NMF: A unified approach to twosided testing of micro array data

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Consensus NMF A unified approach to two-sided
testing of micro array data

• Paul Fogel, Consultant, Paris, France
• S. Stanley Young, National Institute of
  Statistical Sciences
• Post-Genomic workshop, Rennes, France
• February 1, 2008

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Principle

• Tests of means of several variables.
• Variables are ordered according to a
  data-dependent criterion and tested in this
  succession without alpha-adjustment until the
  first non-significant test.

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Data-Driven ordering of Hypothesis

• Simple methods that ignore correlation structure
• Sums of Squares (Kropf Lauter)
• Matrix Factorization methods
• Singular value decomposition (SVD)
• Non-negative matrix factorization (NMF)
• Consensus NMF

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Matrix FactorizationKey Papers

• Good (1969) Technometrics SVD.
• Liu et al. (2003) PNAS rSVD.
• Lee and Seung (1999) Nature NMF.
• Brunet et al. (2004) PNAS Micro array.
• Fogel et al. (2007) Bioinformatics Micro
  array.

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Non-negative matrix factorization Sum of
positive parts

• ? Identifies only up-regulated genes.

W
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Consensus NMF Simultaneous factorization of X
and 1/X

• ? Identifies both up- and down-regulated genes.

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CNMF Algorithm

• Stepwise approach implementing standard NMF
  updating rules at each step
• Run standard NMF, ignoring block information, to
  obtain initial consensus row factors W and
  block-wise column factors Hb.

• Calculate Consensus W between the Wbs (see
  below).
• Go to 2. until convergence.

• Update H from W.
• For each block Xb, update Wb from Hb and scale Wb
  to 1.

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Building the consensus

• To calculate the consensus row factors, we run
  one iteration of NMF in order to factorize the
  concatenated matrix of row factors W1,,B
  W1W2WB W I1,,B
• Start with previous consensus W and I1,,B
  I1I2IB with I1I2IBI where I is the
  K?K Identity matrix.
• Update H.
• Update W and scale to 1.

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Simulated experiment

• Simulate a micro array experiment
• One normal group,
• Two treated groups
• 10 observations per group, with various settings
  for the numbers of regulated genes.
• Up and down regulated genes simulated in equal
  proportion.
• Added correlation structure between regulated
  genes.

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Experimental design
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Simulation results
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Real experiment

• RT-PCR experiment, 38 genes, 2 groups
• CNMF factorization sequential testing ?12
  significant genes.
• BH adjustment
• Standard ?1 significant gene.
• Using NMF to cluster genes and BH adjusting by
  cluster ? 9 significant genes!

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Heatmap view

• All significant genes were clustered into
  cluster 1.
• Cluster 1 is smaller ? BH adjustment is less
  conservative.

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Overcoming misordered variables

• Misordered variables may stop the procedure at an
  early state. Possible causes are
• Varying scale of the variables Those having a
  higher scale tend to be top-ranked Scaling is
  necessary.
• Outliers or other sources of high variability.
• Consecutive P-values can be pooled using Fishers
  method to prevent early stopping.

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Other applications of Consensus NMF

• Signal originating from different sources micro
  array, Taqman, proteomics
• FastNMF
• Image analysis
• Large micro array datasets

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NMF Software

• irMF inferential, robust Matrix Factorization
  (JMP script) http//www.niss.org/irMF/
• Array Studio Software package which provides
  state of the art statistics and visualization for
  the analysis of high dimensional quantification
  data (e.g. Microarray or Taqman data). OmicSoft
  Corporation http//www.omicsoft.com