Elasso for Estimating the Signal Dimension in ICA

Independent component analysis is often considered in a framework where the
$p$
observed variables are a mixtures of only
$d < p$
latent independent components which are contaminated by white noise. The goal is then to estimate the number of latent components as well as the components itself. Meanwhile several approaches exist to estimate
$d$
which are all are based on the eigenvalues of the covariance matrix. However all these approaches were developed and tested in scenarios where
$p$
is moderately small. If
$p$
is however large the estimation of the eigenvalues suffers. To improve the estimation of
$d$
by better estimation of the eigenvalues we employ the recently suggested Elasso which penalizes the eigenvalue structure and groups them together when possible. We show how the Elasso can be used for estimation of
$d$
and show in simulations and in an example that it is better than the competing methods when
$p$
is large.