# Improving Multi-Label Learning by Correlation Embedding
## 2 Related Works  
In multi-label learning, mining the correlation among labels can provide important information, make the prediction results more accurate, and boost the performance of the model. According to the ways on modeling label correlations, existing multi-label learning algorithm can be divided into three categories, i.e., first-order, second-order, and high-order algorithms. The first-order methods [21; 22] deal with multi-label classification problems without modeling the label correlations. BR [21] is a typical first-order algorithm whose basic idea is to transform a multi-label learning problem into multiple independent binary classification problems. The second-order methods exploit the pairwise relationship between labels [23; 24; 25]. For the high-order methods, the relationship between all class labels or a subset is modeled, such as [26; 27; 28]. For example, the classifier chain (CC) [29] is a chain algorithm that uses a vector of class labels as additional instance attributes to model high-order label correlation. The Probabilistic Classifier Chain (PCC) [30] is a probabilistic version of CC. LELC [31] combines label embedding and label correlation to solve multi-label text classification problems. HIDDEN [32] learns the hierarchical multi-label classification based on the joint learning of document classifier and label embedding. ELM-LMF [33] generates the latent label matrix and \(k\)-label dependency matrix based on the label matrix decomposition. CLP-RNN [34] is a multi-label classification method that allows the selection of dynamic and context-dependent label ordering based on label embedding. The MLL-FLSDR [20] algorithm is a multi-label learning method for solving the problem with many labels and features based on the label embedding, which reduces the dimension in both feature space and label space. The second-order methods deal with the multi-label learning problem by exploring the pairwise relationship between the labels that can be divided into two types. First, the second-order methods incorporate the classification criteria ranking loss into the objective function of multi-label learning, such as Rank-SVM [23], MIMLfast [24], and LSEP [25]. Second, the second-order methods constrain the label correlations to the model coefficients or outputs, such as [11; 35; 36; 37; 38]. LLSF [35] used the correlation between the labels to learn specific label features for multi-label learning. LSF-CI [36] is a multi-label feature multi-label learning method which considered the relevant information of the label space and the feature space simultaneously. There are also some algorithms that tend to investigate global and local label correlations. ML-LOC [11] exploits local pairwise label correlation for multi-label learning. LF-LPLC [37] learns specific label features and exploits local pairwise label correlation for multi-label learning. GRRO [38] is a multi-label feature selection method that exploits the global pairwise label correlation to facilitate the selection of features. These algorithms only utilize positive label correlation between labels, while some of the label are negatively correlated or mutually exclusive with each other. To solve this problem, several algorithms have been proposed to model the negative correlation between labels. For example, the LPLC [39] is a simple and effective Bayesian model to investigate the positive correlation and negative correlation between the labels, and it finds the positive and negative relevance class labels for each label. [PERSON] et al. [40] exploited the local positive and negative correlation between labels through \(k\)NN method. Most of these multi-label learning algorithms model label correlation with external conditions, and may not be able to maintain the correlation structure of labels well. Dimension reduction is a fundamental pre-processing procedure for high-dimensional data, and many methods have been proposed for multi-label learning, such as MLDA [41], SSMLDA [42], and MLLS [43].