# Dynamic Online Label Distribution Feature Selection Based on Label Importance and Label Correlation
## 1 Introduction
However, these methods destroy the structural information of the original feature space, blur the physical meaning of the features, and lack semantic interpretation. In contrast to  
Figure 1: Three learning paradigms in the LDL framework. Figure 2: Distribution of facial expressions and emotions. feature extraction methods, feature selection methods do not perform any feature space transformation or mapping; instead, they retain the original spatial structure. Feature selection methods sort the features in the original feature space by importance, select the subspace that best represents the semantic features of that space, and use this subspace to maximally represent the original feature space [19]. Therefore, feature selection methods well preserve the physical meaning of the feature space, which is an advantage of feature extraction methods [20]. From the perspective of interaction with learning algorithms, existing MLL feature selection algorithms are mainly divided into three types: filtering, wrapping, and embedding [21]. All types have different relative advantages. Filtering methods are typically more efficient, less computationally expensive, and more general than embedding and wrapping methods; therefore, this work focuses on filtering methods. In the past few decades, many feature selection algorithms have been proposed for label distribution learning. In related studies [22; 23], these methods were used to consider the correlation between features and labels based on fuzzy rough sets. In addition, because of the correlation between labels, the performance of label distribution models depends largely on label correlation. For example, the method in [24] considers label correlation to reduce data dimensionality, that is, it leverages the assumption that all samples share the same label correlation. However, for different sample groups in practical applications, the corresponding label correlation between random variables is an effective indicator for evaluating the discriminative ability of candidate features in the feature selection process. Alternatively, when dealing with problems related to uncertainty, rough set theory [25; 26] naturally has many advantages and has been widely used in SLL or MLL feature selection algorithms [27; 28]. [PERSON] et al. [29] designed a parallel feature selection method based on neighborhood rough sets (NRSs), which considers the partial order between features and values. [PERSON] et al. [30] proposed a generalized unsupervised feature selection model based on fuzzy rough sets. However, to the best of our knowledge, there are relatively few feature selection methods based on rough set theory for label distribution. The main problem faced by rough sets in dealing with label distribution feature selection is how to deal with distributed labels. In most practical applications of LDL, the feature space is usually uncertain, and the number of samples for each feature increases gradually over time, just like a stream of feature vectors. Such features are called streaming features. For example, on the social networking platform Twitter, hot topics change dynamically over time. When a hot topic appears, it is always accompanied by a set of new keywords. These fresh keywords can be used as key features to distinguish hot topics. Streaming feature selection assumes that features arrive dynamically over time [31] and performs feature selection when each feature arrives to always maintain the optimal subset of features [32; 33]. So far, there have been many methods for processing streaming features. For example, [PERSON] et al. [34] proposed using global features to process streaming feature data, theoretically analyzed the pairwise correlation between features in the currently selected feature subset, and solved the streaming feature problem using online pairwise comparison techniques. NRS can handle mixed types of data without destroying the neighborhood and sequential structure of the data [35].