  Conventional multi-label classification (MLC) methods assume that all samples
are fully labeled and identically distributed. Unfortunately, this assumption
is unrealistic in large-scale MLC data that has long-tailed (LT) distribution
and partial labels (PL). To address the problem, we introduce a novel task,
Partial labeling and Long-Tailed Multi-Label Classification (PLT-MLC), to
jointly consider the above two imperfect learning environments. Not
surprisingly, we find that most LT-MLC and PL-MLC approaches fail to solve the
PLT-MLC, resulting in significant performance degradation on the two proposed
PLT-MLC benchmarks. Therefore, we propose an end-to-end learning framework:
\textbf{CO}rrection $\rightarrow$ \textbf{M}odificat\textbf{I}on $\rightarrow$
balan\textbf{C}e, abbreviated as \textbf{\method{}}. Our bootstrapping
philosophy is to simultaneously correct the missing labels (Correction) with
convinced prediction confidence over a class-aware threshold and to learn from
these recall labels during training. We next propose a novel multi-focal
modifier loss that simultaneously addresses head-tail imbalance and
positive-negative imbalance to adaptively modify the attention to different
samples (Modification) under the LT class distribution. In addition, we develop
a balanced training strategy by distilling the model's learning effect from
head and tail samples, and thus design a balanced classifier (Balance)
conditioned on the head and tail learning effect to maintain stable performance
for all samples. Our experimental study shows that the proposed \method{}
significantly outperforms general MLC, LT-MLC and PL-MLC methods in terms of
effectiveness and robustness on our newly created PLT-MLC datasets.
