  Bipartite data is common in data engineering and brings unique challenges,
particularly when it comes to clustering tasks that impose on strong structural
assumptions. This work presents an unsupervised method for assessing similarity
in bipartite data. Similar to some co-clustering methods, the method is based
on regular equivalence in graphs. The algorithm uses spectral properties of a
bipartite adjacency matrix to estimate similarity in both dimensions. The
method is reflexive in that similarity in one dimension is used to inform
similarity in the other. Reflexive regular equivalence can also use the
structure of transitivities -- in a network sense -- the contribution of which
is controlled by the algorithm's only free-parameter, $\alpha$. The method is
completely unsupervised and can be used to validate assumptions of
co-similarity, which are required but often untested, in co-clustering
analyses. Three variants of the method with different normalizations are tested
on synthetic data. The method is found to be robust to noise and well-suited to
asymmetric co-similar structure, making it particularly informative for cluster
analysis and recommendation in bipartite data of unknown structure. In
experiments, the convergence and speed of the algorithm are found to be stable
for different levels of noise. Real-world data from a network of malaria genes
are analyzed, where the similarity produced by the reflexive method is shown to
out-perform other measures' ability to correctly classify genes.
