  Canonical Correlation Analysis (CCA) is a multivariate technique that takes
two datasets and forms the most highly correlated possible pairs of linear
combinations between them. Each subsequent pair of linear combinations is
orthogonal to the preceding pair, meaning that new information is gleaned from
each pair. By looking at the magnitude of coefficient values, we can find out
which variables can be grouped together, thus better understanding multiple
interactions that are otherwise difficult to compute or grasp intuitively.
  CCA appears to have quite powerful applications to high throughput data, as
we can use it to discover, for example, relationships between gene expression
and gene copy number variation. One of the biggest problems of CCA is that the
number of variables (often upwards of 10,000) makes biological interpretation
of linear combinations nearly impossible. To limit variable output, we have
employed a method known as Sparse Canonical Correlation Analysis (SCCA), while
adding estimation which is resistant to extreme observations or other types of
deviant data. In this paper, we have demonstrated the success of resistant
estimation in variable selection using SCCA. Additionally, we have used SCCA to
find multiple canonical pairs for extended knowledge about the datasets at
hand. Again, using resistant estimators provided more accurate estimates than
standard estimators in the multiple canonical correlation setting.
  R code is available and documented at https://github.com/hardin47/rmscca.
