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 data with high dimensionality often occurs, which will produce large time and energy overheads when directly used in classification tasks. To solve this problem, a novel algorithm called multi-label dimensionality reduction via semi-supervised discriminant analysis (MSDA) was proposed. It was expected to derive an objective discriminant function as smooth as possible on the data manifold by multi-label learning and semi-supervised learning. By virtue of the latent imformation, which was provided by the graph weighted matrix of sample attributes and the similarity correlation matrix of partial sample labels, MSDA readily made the separability between different classes achieve maximization and estimated the intrinsic geometric structure in the lower manifold space by employing unlabeled data. Extensive experimental results on several real multi-label datasets show that after dimensionality reduction using MSDA, the average classification accuracy is about 9.71 higher than that of other algorithms, and several evaluation metrices like Hamming-loss are also superior to those of other dimensionality reduction methods. Multi-label data with high dimensionality arise frequently in data mining and machine learning. It is not only time consuming but also computationally unreliable when we use high-dimensional data directly. Supervised dimensionality reduction approaches are based on the assumption that there are large amounts of labeled data. It is infeasible to label a large number of training samples in practice especially in multi-label learning. To address these challenges, we propose a novel algorithm, namely Semi-Supervised Multi-Label Dimensionality Reduction (SSMLDR), which can utilize the information from both labeled data and unlabeled data in an effective way. First, the proposed algorithm enlarges the multi-label information from the labeled data to the unlabeled data through a special designed label propagation method. It then learns a transformation matrix to perform dimensionality reduction by incorporating the enlarged multi-label information. Extensive experiments on a broad range of datasets validate the effectiveness of our approach against other well-established algorithms. Kernel canonical correlation analysis (KCCA) is a general technique for subspace learning that incorporates principal components analysis (PCA) and Fisher linear discriminant analysis (LDA) as special cases. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying process that generates the data and can ignore high-variance noise directions. However, for data where acquisition in one or more modalities is expensive or otherwise limited, KCCA may suffer from small sample effects. We propose to use semi-supervised Laplacian regularization to utilize data that are present in only one modality. This approach is able to find highly correlated directions that also lie along the data manifold, resulting in a more robust estimate of correlated subspaces. Functional magnetic resonance imaging (fMRI) acquired data are naturally amenable to subspace techniques as data are well aligned. fMRI data of the human brain are a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing. Like other machine learning paradigms, multi-label learning also suffers from the curse of dimensionality problem. Multi-label dimensionality reduction can alleviate the problem but they generally ask for sufficient labeled samples. Nevertheless, we often may only have scarce labeled samples and abundant unlabeled samples. In this paper, we propose a @math emi-supervised @math ulti-label @math imensionality @math eduction based on @math ependence @math aximization approach (SMDRdm in short). SDMRdm assumes the semantic similarity and feature similarity of multi-label samples are inter-depended. SMDRdm first applies label propagation on a neighborhood graph composed with labeled and unlabeled samples to obtain the soft labels of unlabeled samples, and then measures the semantic similarity between all the training samples (including unlabeled ones) based on these soft labels and available labels of labeled samples. Next, it measures the feature similarity between samples in the subspace projected by the target projective matrix, instead of the original high-dimensional feature space. After that, it maximizes the dependence between these two types of similarities and incorporates the dependence into linear discriminant analysis to optimize the target projective matrix. Experiments on publicly accessible multi-label data sets demonstrate that SMDRdm achieves more prominent results than other related approaches across various evaluation metrics. In addition, the empirical study also shows the semantic similarity between samples derived from soft labels works better than that derived from scarce available labels.