@ARTICLE\{IMM2009-05806,
    author       = "M. M{\o}rup and L. K. Hansen",
    title        = "Automatic Relevance Determination for Multiway Models",
    year         = "2009",
    pages        = "352 - 363",
    journal      = "Journal of Chemometrics, Special Issue: In Honor of Professor Richard A. Harshman",
    volume       = "23",
    editor       = "",
    number       = "7-8",
    publisher    = "John Wiley \& Sons, Ltd",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5806-full.html",
    abstract     = "Estimating the adequate number of components is an important yet difficult
problem in multi-way modelling. We demonstrate how a Bayesian framework
for model selection based on Automatic Relevance Determination (ARD) can be
adapted to the Tucker and {CP} models. By assigning priors for the model parameters
and learning the hyperparameters of these priors the method is able to turn
off excess components and simplify the core structure at a computational cost of
fitting the conventional Tucker/{CP} model. To investigate the impact of the choice
of priors we based the {ARD} on both Laplace and Gaussian priors corresponding
to regularization by the sparsity promoting l1-norm and the conventional l2-norm,
respectively. While the form of the priors had limited effect on the results obtained
the {ARD} approach turned out to form a useful, simple, and efficient tool for
selecting the adequate number of components of data within the Tucker and {CP} 
structure. For the Tucker and {CP} model the approach performs better than heuristics
such as the Bayesian Information Criterion, Akaikes Information Criterion,
{DIFFIT} and the numerical convex hull (NumConvHull) while operating only at
the cost of estimating an ordinary {CP}/Tucker model. For the {CP} model the {ARD} 
approach performs almost as well as the core consistency diagnostic. Thus, the
{ARD} framework is a simple yet efficient tool for the estimation of the adequate
number of components in multi-way models. A Matlab implementation of the
proposed algorithm is available for download at www.erpwavelab.org."
}