# Improving Multi-Label Learning by Correlation Embedding
###### Abstract  
In multi-label learning, each object is represented by a single instance and is associated with more than one class labels, where the labels might be correlated with each other. As we all know, exploiting label correlations can definitely improve the performance of a multi-label classification model. Existing methods mainly model label correlations in an indirect way, i.e., adding extra constraints on the coefficients or outputs of a model based on a pre-learned label correlation graph. Meanwhile, the high dimension of the feature space also poses great challenges to multi-label learning, such as high time and memory costs. To solve the above mentioned issues, in this paper, we propose a new approach for Multi-Label Learning by Correlation Embedding, namely MLLCE, where the feature space dimension reduction and the multi-label classification are integrated into a unified framework. Specifically, we project the original high-dimensional feature space to a low-dimensional latent space by a mapping matrix. To model label correlation, we learn an embedding matrix from the pre-defined label correlation graph by graph embedding. Then, we construct a multi-label classifier from the low-dimensional latent feature space to the label space, where the embedding matrix is utilized as the model coefficients. Finally, we extend the proposed method MLLCE to the nonlinear version, i.e., NL-MLLCE. The comparison experiment with the state-of-the-art approaches shows that the proposed method MLLCE has a competitive performance in multi-label learning. multi-label learning; label correlation; label embedding +
Footnote †: journal: Medical  
is proposed, which can find the latent class labels in the training data. DLCL exploits the correlation between known and latent class labels to enhance the performance of the classifier. The Maximal Correlation Embedding Network (MCEN) uses the label similarity by embedding the maximum correlations in the label space to solve the problem of missing labels [16]. MLC-EBMD [17] introduces a multi-label classification framework based on Boolean matrix decomposition to improve the ability to predict labels in high-dimensional label space, and it also performs dimension reduction in the feature space. The aforementioned methods definitely enhance the prediction accuracy of the multi-label algorithm by resolving and using the correlation of label. These methods on modeling label correlation mainly use either popular regular constraints, which means that any two labels with a strong relationship are assigned to similar model coefficients, or label ranking. It is noted that these methods mainly model label correlations in an indirect way, i.e., adding extra constraints on the coefficients or outputs of a multi-label classification model based on a pre-learned label correlation graph. However, in such an indirect way on modeling label correlation, the inherent correlations between different labels will not be well kept. It would be better if a direct way could be proposed. Moreover, in the environment of big data, it is convenient to collect a massive amount of data. However, the curse of dimension has brought great obstacles to multi-label learning.Therefore, it is wise to construct learning models in the low-dimensional feature and label space [18; 19; 20]. To solve the above mentioned issues, in this paper, we propose a new approach for Multi-Label Learning by Correlation Embedding, namely MLLCE, where the feature space dimension reduction and the multi-label classification are integrated into a unified framework. First, we project the original high-dimensional feature space to a low-dimensional latent space by a mapping matrix. To model label correlation, we learn an embedding matrix from the pre-defined label correlation graph by graph embedding. Then, we use the embedding matrix as the model coefficients to construct a multi-label classifier from the low-dimensional latent feature space to the label space.