  A matrix completion problem, which aims to recover a complete matrix from its
partial observations, is one of the important problems in the machine learning
field and has been studied actively. However, there is a discrepancy between
the mainstream problem setting, which assumes continuous-valued observations,
and some practical applications such as recommendation systems and SNS link
predictions where observations take discrete or even binary values. To cope
with this problem, Davenport et al. (2014) proposed a binary matrix completion
(BMC) problem, where observations are quantized into binary values. Hsieh et
al. (2015) proposed a PU (Positive and Unlabeled) matrix completion problem,
which is an extension of the BMC problem. This problem targets the setting
where we cannot observe negative values, such as SNS link predictions. In the
construction of their method for this setting, they introduced a methodology of
the classification problem, regarding each matrix entry as a sample. Their
risk, which defines losses over unobserved entries as well, indicates the
possibility of the use of unobserved entries. In this paper, motivated by a
semi-supervised classification method recently proposed by Sakai et al. (2017),
we develop a method for the BMC problem which can use all of positive,
negative, and unobserved entries, by combining the risks of Davenport et al.
(2014) and Hsieh et al. (2015). To the best of our knowledge, this is the first
BMC method which exploits all kinds of matrix entries. We experimentally show
that an appropriate mixture of risks improves the performance.
