Effectively and efficiently mining valuable clustering patterns is a challenging problem when handling large-scale data from diverse sources. Existing approaches adopt anchor graph learning or binary representation embedding to reduce computational complexity. Normally, anchor graph learning can not directly obtain the clustering assignment except adopt the post-processing stage, such as graph cut or k-means clustering. The binary representation embedding neglects the structure information in Hamming space. In order to overcome these limitations, this paper proposes a novel, effective, and efficient angular reconstructive discrete embedding method with fusion similarity for a multi-view clustering (AFMC) that can jointly learn the global and local structure preserving binary representation and clustering assignment. Specifically, we propose to use angular reconstructive error minimization to maintain the global similarity correlation of binary representations of heterogeneous features in a common Hamming space. Moreover, we design a multi-view discrete ridge regression with fusion similarity term to handle the out-of-sample problem and preserve the local manifold structure. In addition, we propose an efficient optimization algorithm with linear computational complexity to solve the non-convex and non-smooth objective function. The experimental results demonstrate that AFMC outperforms several state-of-the-art large-scale multi-view clustering methods.

Multiview clustering (MVC) aims to integrate multiple related but different views of data to achieve more accurate clustering performance. Contrastive learning has found many applications in MVC due to its successful performance in unsupervised visual representation learning. However, existing MVC methods based on contrastive learning overlook the potential of high similarity nearest neighbors as positive pairs. In addition, these methods do not capture the multilevel (i.e., cluster, instance, and prototype levels) representational structure that naturally exists in multiview datasets. These limitations could further hinder the structural compactness of learned multiview representations. To address these issues, we propose a novel end-to-end deep MVC method called multilevel contrastive MVC (MCMC) with dual self-supervised learning (DSL). Specifically, we first treat the nearest neighbors of an object from the latent subspace as the positive pairs for multiview contrastive loss, which improves the compactness of the representation at the instance level. Second, we perform multilevel contrastive learning (MCL) on clusters, instances, and prototypes to capture the multilevel representational structure underlying the multiview data in the latent space. In addition, we learn consistent cluster assignments for MVC by adopting a DSL method to associate different level structural representations. The evaluation experiment showed that MCMC can achieve intracluster compactness, intercluster separability, and higher accuracy (ACC) in clustering performance. Our code is available at https://github.com/bianjt-morning/MCMC.

Principal component analysis (PCA) is one of the most successful unsupervised subspace learning methods and has been used in many practical applications. To deal with the outliers in real-world data, robust principal analysis models based on various measure are proposed. However, conventional PCA models can only transform features to unknown subspace for dimensionality reduction and cannot perform features’ selection task. In this article, we propose a novel robust PCA (RPCA) model to mitigate the impact of outliers and conduct feature selection, simultaneously. First, we adopt$\sigma $-norm as reconstruction error (RE), which plays an important role in robust reconstruction. Second, to conduct feature selection task, we apply$\ell _{2,0}$-norm constraint to subspace projection. Furthermore, an efficient iterative optimization algorithm is proposed to solve the objective function with nonconvex and nonsmooth constraint. Extensive experiments conducted on several real-world datasets demonstrate the effectiveness and superiority of the proposed feature selection model.

In the field of data mining, how to deal with high-dimensional data is an inevitable topic. Since it does not rely on labels, unsupervised feature selection has attracted a lot of attention. The performance of spectral-based unsupervised methods depends on the quality of the constructed similarity matrix, which is used to depict the intrinsic structure of data. However, real-world data often contain plenty of noise features, making the similarity matrix constructed by original data cannot be completely reliable. Worse still, the size of a similarity matrix expands rapidly as the number of samples rises, making the computational cost increase significantly. To solve this problem, a simple and efficient unsupervised model is proposed to perform feature selection. We formulate PCA as a reconstruction error minimization problem, and incorporate a L2,p-norm regularization term to make the projection matrix sparse. The learned row-sparse and orthogonal projection matrix is used to select discriminative features. Then, we present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically. Finally, experiments on both synthetic and real-world data sets demonstrate the effectiveness of our proposed method.

In recent decades, unsupervised feature selection methods have become increasingly popular. Nevertheless, most of the existing unsupervised feature selection methods suffer from two major problems that lead to suboptimal solutions. Many methods impose a hard linear projection constraint on original data, which is overly strict in nature and not suitable for dealing with data sampled from nonlinear manifolds. Second, most existing methods usel2,p-norm (02S and SF2SOG, which can simultaneously learn optimal flexible projections and obtain an orthogonal sparse projection to directly select discriminative features by applyingl2,0-norm constraint. Moreover, we propose to explore the local structure of flexible embedding through preserving the manifold structure of original data and adaptively constructing an optimal graph in subspace. Thirdly, the novel iterative optimization algorithms are presented to solve objective functions guaranteeing convergence theoretically. Various evaluation experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of our proposed methods.

Feature selection is an important and effective data preprocessing method, which can remove the noise and redundant features while retaining the relevant and discriminative features in high-dimensional data. In real-world applications, the relationships between data samples and their labels are usually nonlinear. However, most of the existing feature selection models focus on learning a linear transformation matrix, which cannot capture such a nonlinear structure in practice and will degrade the performance of downstream tasks. To address the issue, we propose a novel nonlinear feature selection method to select those most relevant and discriminative features in high-dimensional dataset. Specifically, our method learns the nonlinear structure of high-dimensional data by a neural network with cross entropy loss function, and then using the structured sparsity norm such as$\ell _{2,p}$-norm to regularize the weights matrix connecting the input layer and the first hidden layer of the neural network model to learn weight of each feature. Therefore, a structural sparse weights matrix is obtained by conducting nonlinear learning based on a neural network with structured sparsity regularization. Then, we use the gradient descent method to achieve the optimal solution of the proposed model. Evaluating the experimental results on several synthetic datasets and real-world datasets shows the effectiveness and superiority of the proposed nonlinear feature selection model.

Graph-based subspace learning has been widely used in various applications as the rapid growth of data dimension, while the graph is constructed by affinity matrix of input data. However, it is difficult for these subspace learning methods to preserve the intrinsic local structure of data with the high-dimensional noise. To address this problem, we proposed a novel unsupervised dimensionality reduction approach named unsupervised subspace learning with flexible neighboring (USFN). We learn a similarity graph by adaptive probabilistic neighborhood learning process to preserve the manifold structure of high-dimensional data. In addition, we utilize the flexible neighboring to learn projection and latent representation of manifold structure of high-dimensional data to remove the impact of noise. The adaptive similarity graph and latent representation are jointly learned by integrating adaptive probabilistic neighborhood learning and manifold residue term into a unified objection function. The experimental results on synthetic and real-world datasets demonstrate the performance of the proposed unsupervised subspace learning USFN method.

Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned into clusters by using membership matrix with sparse constraint. In addition,$\ell _{2, 1}$-norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method.