Abstract Noisy labeled data represent a rich source of information that often are easily accessible and cheap to obtain, but label noise might also have many negative consequences if not accounted for. How to fully utilize noisy labels has been studied extensively within the framework of standard supervised machine learning over a period of several decades. However, very little research has been conducted on solving the challenge posed by noisy labels in non-standard settings. This includes situations where only a fraction of the samples are labeled (semi-supervised) and each high-dimensional sample is associated with multiple labels. In this work, we present a novel semi-supervised and multi-label dimensionality reduction method that effectively utilizes information from both noisy multi-labels and unlabeled data. With the proposed Noisy multi-label semi-supervised dimensionality reduction (NMLSDR) method, the noisy multi-labels are denoised and unlabeled data are labeled simultaneously via a specially designed label propagation algorithm. NMLSDR then learns a projection matrix for reducing the dimensionality by maximizing the dependence between the enlarged and denoised multi-label space and the features in the projected space. Extensive experiments on synthetic data, benchmark datasets, as well as a real-world case study, demonstrate the effectiveness of the proposed algorithm and show that it outperforms state-of-the-art multi-label feature extraction algorithms.
 Multi-label problems arise frequently in image and video annotations, and many other related applications such as multi-topic text categorization, music classification, etc. Like other computer vision tasks, multi-label image and video annotations also suffer from the difficulty of high dimensionality because images often have a large number of features. Linear discriminant analysis (LDA) is a well-known method for dimensionality reduction. However, the classical Linear Discriminant Analysis (LDA) only works for single-label multi-class classifications and cannot be directly applied to multi-label multi-class classifications. It is desirable to naturally generalize the classical LDA to multi-label formulations. At the same time, multi-label data present a new opportunity to improve classification accuracy through label correlations, which are absent in single-label data. In this work, we propose a novel Multi-label Linear Discriminant Analysis (MLDA) method to take advantage of label correlations and explore the powerful classification capability of the classical LDA to deal with multi-label multi-class problems. Extensive experimental evaluations on five public multi-label data sets demonstrate excellent performance of our method. Linear discriminant analysis (LDA) is one of the most popular dimension reduction methods, but it is originally focused on a single-labeled problem. In this paper, we derive the formulation for applying LDA for a multi-labeled problem. We also propose a generalized LDA algorithm which is effective in a high dimensional multi-labeled problem. Experimental results demonstrate that by considering multi-labeled structure, LDA can achieve computational efficiency and also improve classification performances.  Abstract Linear discriminant analysis (LDA) is one of the most popular single-label (multi-class) feature extraction techniques. For multi-label case, two slightly different generalized versions have been introduced independently. We argue whether there exists a framework to unify such two multi-label LDA methods and to derive more well-performed multi-label LDA techniques further. In this paper, we build a weighted multi-label LDA framework (wMLDA) to consolidate two existing multi-label LDA-type methods with binary and correlation-based weight forms, and further collect two additional weight forms with entropy and fuzzy principles. To exploit both label and feature information more sufficiently, via maximizing dependence based on Hilbert–Schmidt independence criterion, a novel dependence-based weight form is proposed, which is formulated as a non-convex quadratic programing problem with l 1 -norm and non-negative constraints and then is solved by random block coordinate descent method with a linear convergence rate. Experiments on ten data sets illustrate that our dependence-based wMLDA works the best, and five wMLDA-type algorithms are superior to canonical correlation analysis and multi-label dimensionality reduction via dependency maximization, according to five multi-label classification performance measures and Wilcoxon statistical test. Multi-label classification refers to learning tasks with each instance belonging to one or more classes simultaneously. It arose from real-world applications such as information retrieval, text categorization and functional genomics. Currently, most of the multi-label learning methods use the strategy called binary relevance, which constructs a classifier for each unique label by grouping data into positives (examples with this label) and negatives (examples without this label). With binary relevance, an example with multiple labels is considered as a positive data for each label it belongs to. For some classes, this data point may behave like an outlier confusing classifiers, especially in the cases of well-separated classes. In this paper, we first introduce a new strategy called soft relevance, where each multi-label example is assigned a relevance score to the labels it belongs to. This soft relevance is then employed in a voting function used in a k nearest neighbor classifier. Furthermore, a voting-margin ratio is introduced to the k nearest neighbor classifier for better performance. We compare the proposed method to other multi-label learning methods over three multi-label datasets and demonstrate that the proposed method provides an effective way to multi-label learning.  Feature selection on multi-label documents for automatic text categorization is an under-explored research area. This paper presents a systematic document transformation framework, whereby the multi-label documents are transformed into single-label documents before applying standard feature selection algorithms, to solve the multi-label feature selection problem. Under this framework, we undertake a comparative study on four intuitive document transformation approaches and propose a novel approach called entropy-based label assignment (ELA), which assigns the labels weights to a multi-label document based on label entropy. Three standard feature selection algorithms are utilized for evaluating the document transformation approaches in order to verify its impact on multi-class text categorization problems. Using a SVM classifier and two multi-label evaluation benchmark text collections, we show that the choice of document transformation approaches can significantly influence the performance of multi-class categorization and that our proposed document transformation approach ELA can achieve better performance than all other approaches. 