  Latent block models are used for probabilistic biclustering, which is shown
to be an effective method for analyzing various relational data sets. However,
there has been no statistical test method for determining the row and column
cluster numbers of latent block models. Recent studies have constructed
statistical-test-based methods for stochastic block models, which assume that
the observed matrix is a square symmetric matrix and that the cluster
assignments are the same for rows and columns. In this study, we developed a
new goodness-of-fit test for latent block models to test whether an observed
data matrix fits a given set of row and column cluster numbers, or it consists
of more clusters in at least one direction of the row and the column. To
construct the test method, we used a result from the random matrix theory for a
sample covariance matrix. We experimentally demonstrated the effectiveness of
the proposed method by showing the asymptotic behavior of the test statistic
and measuring the test accuracy.
