  Matrix completion has attracted attention in many fields, including
statistics, applied mathematics, and electrical engineering. Most of the works
focus on the independent sampling models under which the observed entries are
sampled independently. Motivated by applications in the integration of
knowledge graphs derived from multi-source biomedical data such as those from
Electronic Health Records (EHR) and biomedical text, we propose the {\bf
B}lock-wise {\bf O}verlapping {\bf N}oisy {\bf M}atrix {\bf I}ntegration
(BONMI) to treat blockwise missingness of symmetric matrices representing
relatedness between entity pairs. Our idea is to exploit the orthogonal
Procrustes problem to align the eigenspace of the two sub-matrices, then
complete the missing blocks by the inner product of the two low-rank
components. Besides, we prove the statistical rate for the eigenspace of the
underlying matrix, which is comparable to the rate under the independently
missing assumption. Simulation studies show that the method performs well under
a variety of configurations. In the real data analysis, the method is applied
to two tasks: (i) the integrating of several point-wise mutual information
matrices built by English EHR and Chinese medical text data, and (ii) the
machine translation between English and Chinese medical concepts. Our method
shows an advantage over existing methods.
