To determine the appropriate rank automatically, we adopt the Automatic Relevance Determination (ARD) method (Babacan et al., 2012) by imposing a prior on each dimmension (column) of U and V .
we impose the Gaussian priors with variance λ r on the r-th columns of U and V , i.e., u .r and v .r : where IG is an Inverse Gamma distribution for modeling the variance λ r .