# Application of Label Correlation in Multi-Label Classification: A Survey
## 3 Label Correlation Mining Methods
### Label Sequences-Based Methods  
This approach views MLL as a label sequence prediction problem, incorporating label dependencies when constructing the label sequence. The key challenge is how to determine the optimal label sequence. [PERSON] et al. [55] first introduced the Classifier Chains (CC) method in 2011. This approach stacks multiple binary classifiers in a chain structure and incorporates the outputs of all preceding classifiers in the chain as additional information into the feature space of the current classifier, leveraging these new features for training. This chain structure enhances MLL by capturing the implicit dependencies among labels. However, the performance of the CC method is highly sensitive to the order of labels in the chain, and during the prediction phase, error propagation may occur, introducing noise and reducing classification accuracy. To mitigate this drawback, the paper also proposed an ensemble version of the CC method, ECC [55]. The ECC method randomly generates multiple label sequences, calls the CC algorithm multiple times to train multiple classifier chains, and takes the ensemble result of all classifier chains when predicting new samples. Although the ECC method can eliminate the adverse effects of label order, it has a higher time complexity because the multiple binary classifiers on multiple classifier chains in ECC cannot be trained in parallel. To address the issue of label ordering, [PERSON] et al. [56] proposed the MCC method, which uses a Monte Carlo approach to determine label sequences. [PERSON] et al. [57] extended the CC method by introducing the Probabilistic Classifier Chains (PCC) model, aimed at mitigating the error propagation problem while accounting for the conditional probabilities of different label combinations. [PERSON] and [PERSON] [58] optimized the classifier chain order from the perspective of maximizing conditional likelihood. [PERSON] and [PERSON] [59] used dynamic programming techniques to search for the globally optimal label order for CC. Since searching all different label orders to find the global optimum is very time-consuming, they further proposed a Greedy Classifier Chain algorithm to find a locally optimal label order to accelerate the search speed. It is important to emphasize that in MLC, the size of the label set increases exponentially with the number of labels, especially in MLC problems with a large number of labels. For large-scale datasets, traditional multi-label algorithms such as Binary Relevance and classifier chain-based methods incur extremely high computational costs. Therefore, when dealing with MLC problems involving a large number of labels, more efficient algorithms and optimization strategies with lower computational costs are required. To address this issue, [PERSON] et al. [60] proposed a neural network-based solution for MLC, framing the task as a sequence generation problem. They introduced a sequence generation model (SGM) with a novel decoder architecture (as shown in Figure 4). The text sequence \(\mathbf{x}\) is input into a bidirectional LSTM, which encodes it into hidden states. The bidirectional LSTM reads the text sequence from both directions, and then generates the context vector \(\mathbf{c}_{t}\) through the attention mechanism at time step \(t\). The decoder utilizes this context vector, the hidden state from the previous time step, and the embedding vector to generate the hidden state for the current time step, ultimately outputting the probability distribution \(\mathbf{y}_{t}\) through the masked Softmax layer. In this model, the decoder employs LSTM [61] to sequentially generate labels, predicting the next label based on the previously predicted one. As a result, the SGM model leverages the LSTM structure to manage the sequential dependencies among labels while accounting for label correlations. When dealing with a large number of labels, accurately predicting all true labels becomes complex and challenging.