# Dynamic Online Label Distribution Feature Selection Based on Label Importance and Label Correlation
## 1 Introduction  
In the field of machine learning and data mining [1], the problem of label ambiguity is currently a popular research topic. There are currently two relatively mature machine learning paradigms, namely, single-label learning (SLL) and multi-label learning (MLL) [2]. SLL achieves good results in the field of machine learning when the target instance has a clear single-class label. MLL is an extension of SLL. In real life, an object may be associated with several class labels. To intuitively reflect the characteristics of polysemous objects, the most obvious approach is to assign multiple category labels to each example of a polysemous object, that is, to use MLL [3, 4]. Because it is constrained by label semantics, traditional multi-label classification assumes that relevant and irrelevant labels have the same degree of relevance to the description of the example, which obviously does not meet the complex cognitive needs of humans [5]. In layman's terms, MLL only solves the label ambiguity problem of labels associated with the instance. However, in real life, we need to solve the more common and ambiguous scenario of \"how to describe the instance\". For example, in facial-expression emotion recognition, it is more meaningful to understand the degree to which each emotion describes the instance. To solve these problems, a new learning paradigm has been proposed in recent years--label distribution learning (LDL) [6], which is an extension of MLL. The degree of LDL to which each label describes an instance is represented by the corresponding value of the label distribution, called the descriptive degree. This value explicitly indicates the relative importance of the label. Both SLL and MLL can be regarded as special cases of LDL. Figure 1 shows the three learning paradigms within the LDL framework. Figure 2 shows an image described using a label distribution. The label descriptions of \"HAP\", \"SAD\", \"SUR\", \"ANG\", \"DIS\", and \"FER\" in the image are shown in Figure 2. LDL has richer label information and clearly describes the importance of each label [7]. At present, it has been applied in multiple neighborhoods. For example, the adaptive facial recognition proposed by [PERSON] et al., achieved good results by estimating the age of sample characters through LDL [8]. [PERSON] et al., by collecting surveillance video data, used LDL to implement crowd counting applications over a period of time [9], and [PERSON] et al., used LDL to predict box office before movie release by collecting people's opinions on movies [10]. LDL has also been widely used in fields such as emotion recognition and multilingual learning. Similar to traditional SLL and MLL, LDL also faces many challenges. In terms of the data structure of label instances, the problems faced by LDL tasks include a large number of feature dimensions [11], large number of labels [12], label imbalance [13], and streaming features [14]. In LDL tasks, the dimensionality of the data is very large, with usually thousands or tens of thousands of dimensions [15; 16]. This \"curse of dimensionality\" leads to a series of problems such as reduced classification accuracy and generalization ability in high-dimensional space, and it increases the computational cost of many learning algorithms. In addition, too many features may contain redundant or irrelevant features, which may lead to more problems such as the excessive consumption of computing resources and degradation of model performance. To this end, many dimensionality reduction methods have been proposed [17; 18]. However, they are mainly designed for SLL and MLL algorithms, and are rarely suitable for LDL algorithms. Therefore, there is an urgent need to develop new and effective LDL dimensionality reduction methods. There are two main methods for reducing the dimensionality of label distribution: feature extraction and feature selection. Feature extraction methods use space mapping techniques or space transformations to reduce the dimensionality of the feature space.