4 - Central Institute of Brackishwater Aquaculture

National Workshop-cum-Training on llidnformatics and Information Managemant in Aquaculture
3.3.4. Principal Component Analysis of Microarray
Objectives of principal component analysis (PCA) are to discover or to reduce the
dimensionality of the data set and to identify new meaningful underlying
variables. PCA transforms a number of (possibly) correlated variables into a
(smaller) number of uncorrelated variables called principal components. The
basic idea in PCA is to find the components that explain the maximum amount of
variance possible by n linearly transformed components. The first principal
component accounts for as much of the variability in the data as possible, and
each succeeding component accounts for as much of the remaining variability as
possible. PCA can be also applied when other information in addition to the
actual expression levels is available (this applies to SOM and K-means methods
as well).
Fig. 7 An example of principal component analysis. The two most significant
principal components have been selected as the axes of the plot (Source;
Hovatta et. al.)
3.3.5. Correspondence Analysis
Correspondence analysis is an explorative method to study associations between
variables. It directly visualizes associations between genes and hybridizations.
Unlike many other methods, CA does not require any prior choice of parameters.
Like principal components, it displays a low-dimensional projection of the data.
However, in this case, both genes and samples can be projected onto the same
space, revealing associations between them. Correspondence analysis requires
an expression matrix with no missing valu6s. Therefore, any missing values have
to be imputed first. We use the k-nearest neighbors algorithm to impute missing
values. The only user input in the initialization dialog is the desired number of
neighbors for imputation. Genes that lie close to one another on the plot tend to
have similar profiles, regardless of their absolute value. The same is true for
samples. If some genes and samples lie close to one another on the plot, then
these genes are likely to have a high expression in the nearby samples relative
to other samples that are far away on the plot. On the other hand, if a set of
genes are on the opposite side of the plot from a set of samples relative to the