Gene Shaving

1
Gene Shaving Applying PCA

• Identify groups of genes a set of genes using PCA
  which serve as the informative genes to classify
  samples.
• The gene shaving method is also a method of
  clustering genes and sample cells. But unlike
  classic clustering, in this method, one gene
  could belong to more than one cluster.

2
Features of Gene Groups

• The genes in each cluster behave in a similar
  manner, which suggests similar or related
  function among genes
• The cluster centroid shows high variance across
  the samples, which indicates the potential of
  this cluster to distinguish sample classes
• The groups are as much uncorrelated between each
  other (which encourages seeking groups of
  different specification) as possible.

3
Motivation and Details

• We favor subsets of genes that
• All behave in a similar manner (coherence)
• And all show large across the cell lines.
• Given an expression array, we seek a sequence of
  nested gene clusters of size k. has the
  property that the variance of the cluster mean is
  maximum over all clusters of size k.

4
Gene Shaving approach finds the linear
combination of genes having maximal variation
among samples. This linear combination of genes
is viewed as a super gene. The genes having
lowest correlation with the super gene is
removed (shaved). The process is continued until
the subset of genes contains only one gene. This
process produces a sequence of gene blocks, each
containing genes that are similar to one another
and displaying large variance across samples.
A statistical approach Identifies subsets of
genes with coherent expression patterns and large
variation across conditions Gene may belong to
more than one cluster Can be either un-supervised
or supervised
5
Gene Shaving Algorithm-1

• STEP 1. Start with the entire expression data X,
  each row centered to have zero mean.
• STEP 2. Compute the leading principal component
  of the rows of X.
• STEP 3. Shave off the proportion alpha (typically
  10) of the rows having smallest inner-product
  with the leading principal component.
• STEP 4. Repeat step 2 and 3 until only one gene
  remains.

6
Gene Shaving Iteration
7
Gene Shaving Algorithm-2

• STEP 5. This produces a sequence of nested gene
  clusters
• where denotes a cluster of k genes.
  Estimate the optimal cluster size
• STEP 6. Orthogonalize each row of X with respect
  to , the average gene in
• STEP 7. Repeat steps 1-5 above with the
  orthogonalized data, to find the second optimal
  cluster. This process is continued until a
  maximum of M clusters are found, with M chosen
  apriori.

8
Principal Component of the rows
slides
Z1
slide
Super-gene
9
The Gap estimate of cluster size
Vb
Vt
We then select as the optimal number of genes
that value k producing The largest gap
10
Gene Shaving (Cont.)
The first three gene clusters found for the DLCL
data
11
Gene Shaving (Cont.)
Percent of gene variance explained by first j
gene shaving column averages (averages of the
genes in each cluster, j 1,2,... 10) (solid
curve), and by first j principal components
(broken curve). For the shaving results, the
total number of genes in the first j clusters is
also indicated.
12
Gene Shaving ( Cont.)

• Variance plots for real and randomized data. The
  percent variance explained by each cluster, both
  for the original data, and for an average over
  three randomized versions.
• Gap estimates of cluster size. The gap curve,
  which highlights the difference between the pair
  of curves, is shown.

13
References

• Gene Shaving as a method for identifying
  distinct sets of genes with similar expression
  patterns T. Hastie, R. Tibshirani, M.B. Eisen, A
  Alizadeh, R. Levy,L Staudt, W.C Chan, D.Botstein
  and P. Brown. Genome Biology 2000.
  http//genomebiology.com/2000/1/2/research/0003/B
  14.