  Exploiting label correlations is important to multi-label classification.
Previous methods capture the high-order label correlations mainly by
transforming the label matrix to a latent label space with low-rank matrix
factorization. However, the label matrix is generally a full-rank or
approximate full-rank matrix, making the low-rank factorization inappropriate.
Besides, in the latent space, the label correlations will become implicit. To
this end, we propose a simple yet effective method to depict the high-order
label correlations explicitly, and at the same time maintain the high-rank of
the label matrix. Moreover, we estimate the label correlations and infer model
parameters simultaneously via the local geometric structure of the input to
achieve mutual enhancement. Comparative studies over twelve benchmark data sets
validate the effectiveness of the proposed algorithm in multi-label
classification. The exploited high-order label correlations are consistent with
common sense empirically. Our code is publicly available at
https://github.com/Chongjie-Si/HOMI.
