You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Multi-view high-dimensional data become increasingly popular in the big data era. Feature selection is a useful technique for alleviating the curse of dimensionality in multi-view learning. In this paper, we study unsupervised feature selection for multi-view data, as class labels are usually expensive to obtain. Traditional feature selection methods are mostly designed for single-view data and cannot fully exploit the rich information from multi-view data. Existing multi-view feature selection methods are usually based on noisy cluster labels which might not preserve sufficient information from multi-view data. To better utilize multi-view information, we propose a method, CDMA-FS, to select features for each view by performing alignment on a cross diffused matrix. We formulate it as a constrained optimization problem and solve it using Quasi-Newton based method. Experiments results on four real-world datasets show that the proposed method is more effective than the state-of-the-art methods in multi-view setting.

Cited Abstract(s):
[1]: The explosive popularity of social media produces mountains of high-dimensional data and the nature of social media also determines that its data is often unlabelled, noisy and partial, presenting new challenges to feature selection. Social media data can be represented by heterogeneous feature spaces in the form of multiple views. In general, multiple views can be complementary and, when used together, can help handle noisy and partial data for any single-view feature selection. These unique challenges and properties motivate us to develop a novel feature selection framework to handle multi-view social media data. In this paper, we investigate how to exploit relations among views to help each other select relevant features, and propose a novel unsupervised feature selection framework, MVFS, for multiview social media data. We systematically evaluate the proposed framework in multi-view datasets from social media websites and the results demonstrate the effectiveness and potential of MVFS.

[2]: In this paper, we propose an Online unsupervised Multi-View Feature Selection method, OMVFS, which deals with large-scale streaming multi-view data in an online fashion. OMVFS embeds unsupervised feature selection into a clustering algorithm via nonnegative matrix factorization with sparse learning. It further incorporates the graph regularization to preserve the local structure information and help select discriminative features. Instead of storing all the historical data, OMVFS processes the multi-view data chunk by chunk and aggregates all the necessary information into several small matrices. By using the buffering technique, the proposed OMVFS can reduce the computational and storage cost while taking advantage of the structure information. Furthermore, OMVFS can capture the concept drifts in the data streams. Extensive experiments on four real-world datasets show the effectiveness and efficiency of the proposed OMVFS method. More importantly, OMVFS is about 100 times faster than the off-line methods.

[3]: To reveal and leverage the correlated and complemental information between different views, a great amount of multi-view learning algorithms have been proposed in recent years. However, unsupervised feature selection in multi-view learning is still a challenge due to lack of data labels that could be utilized to select the discriminative features. Moreover, most of the traditional feature selection methods are developed for the single-view data, and are not directly applicable to the multi-view data. Therefore, we propose an unsupervised learning method called Adaptive Unsupervised Multi-view Feature Selection (AUMFS) in this paper. AUMFS attempts to jointly utilize three kinds of vital information, i.e., data cluster structure, data similarity and the correlations between different views, contained in the original data together for feature selection. To achieve this goal, a robust sparse regression model with the l2,1-norm penalty is introduced to predict data cluster labels, and at the same time, multiple view-dependent visual similar graphs are constructed to flexibly model the visual similarity in each view. Then, AUMFS integrates data cluster labels prediction and adaptive multi-view visual similar graph learning into a unified framework. To solve the objective function of AUMFS, a simple yet efficient iterative method is proposed. We apply AUMFS to three visual concept recognition applications (i.e., social image concept recognition, object recognition and video-based human action recognition) on four benchmark datasets. Experimental results show the proposed method significantly outperforms several state-of-the-art feature selection methods. More importantly, our method is not very sensitive to the parameters and the optimization method converges very fast.

[4]: In this paper, a new unsupervised learning algorithm, namely Nonnegative Discriminative Feature Selection (NDFS), is proposed. To exploit the discriminative information in unsupervised scenarios, we perform spectral clustering to learn the cluster labels of the input samples, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables NDFS to select the most discriminative features. To learn more accurate cluster labels, a nonnegative constraint is explicitly imposed to the class indicators. To reduce the redundant or even noisy features, l2,1-norm minimization constraint is added into the objective function, which guarantees the feature selection matrix sparse in rows. Our algorithm exploits the discriminative information and feature correlation simultaneously to select a better feature subset. A simple yet efficient iterative algorithm is designed to optimize the proposed objective function. Experimental results on different real world datasets demonstrate the encouraging performance of our algorithm over the state-of-the-arts.

[5]: Unlabeled high-dimensional text-image web news data are produced every day, presenting new challenges to unsupervised feature selection on multi-view data. State-of-the-art multi-view unsupervised feature selection methods learn pseudo class labels by spectral analysis, which is sensitive to the choice of similarity metric for each view. For text-image data, the raw text itself contains more discriminative information than similarity graph which loses information during construction, and thus the text feature can be directly used for label learning, avoiding information loss as in spectral analysis. We propose a new multi-view unsupervised feature selection method in which image local learning regularized orthogonal nonnegative matrix factorization is used to learn pseudo labels and simultaneously robust joint @math -norm minimization is performed to select discriminative features. Cross-view consensus on pseudo labels can be obtained as much as possible. We systematically evaluate the proposed method in multi-view text-image web news datasets. Our extensive experiments on web news datasets crawled from two major US media channels: CNN and FOXNews demonstrate the efficacy of the new method over state-of-the-art multi-view and single-view unsupervised feature selection methods.

[6]: A new unsupervised feature selection method, i.e., Robust Unsupervised Feature Selection (RUFS), is proposed. Unlike traditional unsupervised feature selection methods, pseudo cluster labels are learned via local learning regularized robust nonnegative matrix factorization. During the label learning process, feature selection is performed simultaneously by robust joint l2,1 norms minimization. Since RUFS utilizes l2,1 norm minimization on processes of both label learning and feature learning, outliers and noise could be effectively handled and redundant or noisy features could be effectively reduced. Our method adopts the advantages of robust non-negative matrix factorization, local learning, and robust feature learning. In order to make RUFS be scalable, we design a (projected) limited-memory BFGS based iterative algorithm to efficiently solve the optimization problem of RUFS in terms of both memory consumption and computation complexity. Experimental results on different benchmark real world datasets show the promising performance of RUFS over the state-of-the-arts.
Recently, several pseudo label-based methods have been extended to multi-view setting [1] [5] [2] via cluster consensus learning. In these approaches, pseudo-labels derived from certain clustering algorithms are required to be the same across different views in order to incorporate multi-view information. For example, adaptive Unsupervised Multi-view Feature Selection (AUMFS) [3] rely on spectral clustering on the combined similarity graphs obtained from different views. Multi-View Feature Selection (MVFS) [1] and MVUFS [5] can be seen as extention of NDFS [4] and RUFS [6] to multi-view feature selection by enforcing consensus on the cluster indicators from different views, respectively. However, they rely on the cluster labels to guide feature selection, and the noisy cluster labels may lead to suboptimal feature selection results. Also, they evaluate features based on linear regression and hence cannot select high-quality features if they are non-linearly correlated with the class labels.