  This work focuses on the problem of multi-label learning with missing labels
(MLML), which aims to label each test instance with multiple class labels given
training instances that have an incomplete/partial set of these labels. The key
point to handle missing labels is propagating the label information from
provided labels to missing labels, through a dependency graph that each label
of each instance is treated as a node. We build this graph by utilizing
different types of label dependencies. Specifically, the instance-level
similarity is served as undirected edges to connect the label nodes across
different instances and the semantic label hierarchy is used as directed edges
to connect different classes. This base graph is referred to as the mixed
dependency graph, as it includes both undirected and directed edges.
Furthermore, we present another two types of label dependencies to connect the
label nodes across different classes. One is the class co-occurrence, which is
also encoded as undirected edges. Combining with the base graph, we obtain a
new mixed graph, called MG-CO (mixed graph with co-occurrence). The other is
the sparse and low rank decomposition of the whole label matrix, to embed
high-order dependencies over all labels. Combining with the base graph, the new
mixed graph is called as MG-SL (mixed graph with sparse and low rank
decomposition). Based on MG-CO and MG-SL, we propose two convex transductive
formulations of the MLML problem, denoted as MLMG-CO and MLMG-SL, respectively.
Two important applications, including image annotation and tag based image
retrieval, can be jointly handled using our proposed methods. Experiments on
benchmark datasets show that our methods give significant improvements in
performance and robustness to missing labels over the state-of-the-art methods.
