  Multi-graph multi-label learning (\textsc{Mgml}) is a supervised learning
framework, which aims to learn a multi-label classifier from a set of labeled
bags each containing a number of graphs. Prior techniques on the \textsc{Mgml}
are developed based on transfering graphs into instances and focus on learning
the unseen labels only at the bag level. In this paper, we propose a
\textit{coarse} and \textit{fine-grained} Multi-graph Multi-label (cfMGML)
learning framework which directly builds the learning model over the graphs and
empowers the label prediction at both the \textit{coarse} (aka. bag) level and
\textit{fine-grained} (aka. graph in each bag) level. In particular, given a
set of labeled multi-graph bags, we design the scoring functions at both graph
and bag levels to model the relevance between the label and data using specific
graph kernels. Meanwhile, we propose a thresholding rank-loss objective
function to rank the labels for the graphs and bags and minimize the
hamming-loss simultaneously at one-step, which aims to addresses the error
accumulation issue in traditional rank-loss algorithms. To tackle the
non-convex optimization problem, we further develop an effective sub-gradient
descent algorithm to handle high-dimensional space computation required in
cfMGML. Experiments over various real-world datasets demonstrate cfMGML
achieves superior performance than the state-of-arts algorithms.
