ac:
Artificial Components for Gene Expression Data
Description
Computes the artificial components for gene expression data between two
conditions for a single time point.
Usage
ac(Z, design)
ac2(Z, design)
Arguments
Z
a numeric matrix or data.frame with $n$ rows and $p$ columns
representing genes' expression levels. The rows of $Z$ correspond
to the genes in the experiment, and the columns correspond to the
replicates. Treatment replicates are to the left, control replicates
to the right.
design
a vector of length $p$ with 1's for the treatment replicates and
2's for the control replicates
$(1, \ldots, 1, 2, \ldots, 2)$.
Value
ac returns a matrix with the artificial components
$\psi[1]$ and $\psi[2]$ in the columns.ac2 returns a matrix with the second artificial component
$\psi[2]$ in the only column.
Details
This function computes the artificial components of Z, based on the
specified design vector. First, the function scales $Z$ so that
its columns have zero mean and unit variance. Then computation of
the artificial components $\psi[1]$ and
$\psi[2]$ is performed as $\psi[1] = Zv[1]$, where $v[1] = (1, \ldots , 1) / sqrt(p)$,
and $\psi[2] = Zv[2]$, where $v[2] = (1,
\ldots , 1, -1, \ldots , -1 ) / sqrt(p*p[1]*(p-p[1]))$. Here,
$p[1]$ is the number of treatment replicates, and
$v[2]$ has $p[1]$ positive and
$p-p[1]$ negative entries.
References
Acosta, J. P. (2015) Strategy for Multivariate Identification
of Differentially Expressed Genes in Microarray Data. Unpublished
MS thesis. Universidad Nacional de Colombia, Bogot\'a.
## Computes the artificial components for the ## phitophthora infestans data at 60 hai.psi <- ac(phytophthora[[4]], c(rep(1,8), rep(2,8)))
plot(x=psi[,1], y=psi[,2])