# An Effective Multi-Label Feature Selection Model Towards Eliminating Noisy Features
## 1 Introduction  
For pattern recognition, feature selection is important for its effectiveness in reducing dimensionality. Feature selection methods are divided into supervised, semi-supervised, and unsupervised ones, according to whether the instances are labeled, partially labeled, or not [1; 2; 3; 4]. For supervised cases, class labels are employed for measuring features' discriminative abilities. Many popular and efficient feature selection methods belong to this group [5; 6; 7; 8; 9; 10]. Supervised methods are further categorized into three well-known models: filter, wrapper, and embedded [11]. In recent years, some hybrid methods have emerged that combine filter and wrapper processes for enhancing performance and reducing computational cost [12; 13]. In another categorization view, existing feature selection approaches can also be grouped to single-label and multi-label ones, whose difference lies in the size of labels that each instance is related with [14]. In single-label FS, instances and labels hold many-to-one connections and the target separability is emphasized in this learning task. With the great potential and success of multi-label learning in many machine learning fields, such as text categorization [15], content annotation [16], and protein location prediction [17], multi-label feature selection has received considerable attention in recent years. We approach the supervised multi-label feature selection in this study. In multi-label learning, label correlations are the key to combining the complicated relationships among instances, which are typically annotated with multiple labels [18; 19]. The mainstream multi-label feature selection strategy is to extract label correlations (via statistical or information-based measurements) and employ them to help find the most remarkable features. A critical issue is, however, this strategy would be trapped by two kinds of features, that is, irrelevant and redundant ones. Irrelevant features represent those lowly discriminative ones. Features of this kind are loosely correlated with learning targets and even may provide misleading information. Compared with irrelevant features, redundant features seem more deceptive. They may exhibit excellent (or comparably superior) performances and mix with remarkable features. Nevertheless, redundant features also lowly contribute to enhancing the discriminative ability of the constructed low-dimensional subspace, because the learning information they provide is redundant with the already distilled information. In general, we regard both irrelevant and redundant features as noisy ones, which may confuse selection processes and compromise the learning performance of downstream tasks. In this paper, we present an effective multi-label feature selection model by embedding label correlations to eliminate noisy features, named ELC. Our major strategy is to keep feature-label space consistent and explore reliable label structures to drive feature selection. Concretely, we qualitatively assess label correlations in the label space and embed them in feature selection. In this way, the label structure information can be maximally preserved in the constructed low-dimensional subspace, and eventually the consistency between feature and label spaces can be achieved. Furthermore, we devise an efficient framework base on the sparse multi-task learning to optimize ELC, which can help ELC find globally optimal solutions and efficiently converge. The major contributions of this paper are as follows:  
* We present a novel multi-label feature selection model to address the issue of noisy features. This model qualitatively measures label correlations and employs feature-label space consistency to steer feature selection. * We devised a compact framework to optimize the proposed model. This framework resorts to the multi-task learning strategy and promises globally optimal solutions and efficient convergence.