Correntropy-Based Multiview Subspace Clustering

Fast Multiview Anchor-Graph Clustering

Due to its high computational complexity, graph-based methods have limited applicability in large-scale multiview clustering tasks. To address this issue, many accelerated algorithms, especially anchor graph-based methods and indicator learning-based methods, have been developed and made a great success. Nevertheless, since the restrictions of the optimization strategy, these accelerated methods still need to approximate the discrete graph-cutting problem to a continuous spectral embedding problem and utilize different discretization strategies to obtain discrete sample categories. To avoid the loss of effectiveness and efficiency caused by the approximation and discretization, we establish a discrete fast multiview anchor graph clustering (FMAGC) model that first constructs an anchor graph of each view and then generates a discrete cluster indicator matrix by solving the discrete multiview graph-cutting problem directly. Since the gradient descent-based method makes it hard to solve this discrete model, we propose a fast coordinate descent-based optimization strategy with linear complexity to solve it without approximating it as a continuous one. Extensive experiments on widely used normal and large-scale multiview datasets show that FMAGC can improve clustering effectiveness and efficiency compared to other state-of-the-art baselines.

Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN2MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN2MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN2MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN2MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN2MSL has achieved better performance in comparison to state-of-the-art methods.

Multi-View Clustering via Nonnegative and Orthogonal Graph Reconstruction

The goal of multi-view clustering is to partition samples into different subsets according to their diverse features. Previous multi-view clustering methods mainly exist two forms: multi-view spectral clustering and multi-view matrix factorization. Although they have shown excellent performance in many occasions, there are still many disadvantages. For example, multi-view spectral clustering usually needs to perform postprocessing. Multi-view matrix factorization directly decomposes the original data features. When the size of features is large, it encounters the expensive time consumption to decompose these data features thoroughly. Therefore, we proposed a novel multi-view clustering approach. The main advantages include the following three aspects: 1) it searches for a common joint graph across multiple views, which fully explores the hidden structure information by utilizing the compatibility among views; 2) the introduced nonnegative constraint manipulates that the final clustering results can be directly obtained; and 3) straightforwardly decomposing the similarity matrix can transform the eigenvalue factorization in spectral clustering with computational complexity O(n³) into the singular value decomposition (SVD) with O(nc²) time cost, where n and c , respectively, denote the numbers of samples and classes. Thus, the computational efficiency can be improved. Moreover, in order to learn a better clustering model, we set that the constructed similarity graph approximates each view affinity graph as close as possible by adding the constraint as the initial affinity matrices own. Furthermore, substantial experiments are conducted, which verifies the superiority of the proposed two clustering methods comparing with single-view clustering approaches and state-of-the-art multi-view clustering methods.

CSMVC: A Multiview Method for Multivariate Time-Series Clustering

Multivariate time-series (MTS) clustering is a fundamental technique in data mining with a wide range of real-world applications. To date, though some approaches have been developed, they suffer from various drawbacks, such as high computational cost or loss of information. Most existing approaches are single-view methods without considering the benefits of mutual-support multiple views. Moreover, due to its data structure, MTS data cannot be handled well by most multiview clustering methods. Toward this end, we propose a consistent and specific non-negative matrix factorization-based multiview clustering (CSMVC) method for MTS clustering. The proposed method constructs a multilayer graph to represent the original MTS data and generates multiple views with a subspace technique. The obtained multiview data are processed through a novel non-negative matrix factorization (NMF) method, which can explore the view-consistent and view-specific information simultaneously. Furthermore, an alternating optimization scheme is proposed to solve the corresponding optimization problem. We conduct extensive experiments on 13 benchmark datasets and the results demonstrate the superiority of our proposed method against other state-of-the-art algorithms under a wide range of evaluation metrics.

Self-Guided Deep Multiview Subspace Clustering via Consensus Affinity Regularization

Multiview subspace clustering (MVSC) leverages the complementary information among different views of multiview data and seeks a consensus subspace clustering result better than that using any individual view. Though proved effective in some cases, existing MVSC methods often obtain unsatisfactory results since they perform subspace analysis with raw features that are often of high dimensions and contain noises. To remedy this, we propose a self-guided deep multiview subspace clustering (SDMSC) model that performs joint deep feature embedding and subspace analysis. SDMSC comprehensively explores multiview data and strives to obtain a consensus data affinity relationship agreed by features from not only all views but also all intermediate embedding spaces. With more constraints being cast, the desirable data affinity relationship is supposed to be more reliably recovered. Besides, to secure effective deep feature embedding without label supervision, we propose to use the data affinity relationship obtained with raw features as the supervision signals to self-guide the embedding process. With this strategy, the risk that our deep clustering model being trapped in bad local minima is reduced, bringing us satisfactory clustering results in a higher possibility. The experiments on seven widely used datasets show the proposed method significantly outperforms the state-of-the-art clustering methods. Our code is available at https://github.com/kailigo/dmvsc.git.

Multiview Subspace Clustering Using Low-Rank Representation

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

Deep Multiview Clustering via Iteratively Self-Supervised Universal and Specific Space Learning

Multiview clustering seeks to partition objects via leveraging cross-view relations to provide a comprehensive description of the same objects. Most existing methods assume that different views are linear transformable or merely sampling from a common latent space. Such rigid assumptions betray reality, thus leading to unsatisfactory performance. To tackle the issue, we propose to learn both common and specific sampling spaces for each view to fully exploit their collaborative representations. The common space corresponds to the universal self-representation basis for all views, while the specific spaces are the view-specific basis accordingly. An iterative self-supervision scheme is conducted to strengthen the learned affinity matrix. The clustering is modeled by a convex optimization. We first solve its linear formulation by the popular scheme. Then, we employ the deep autoencoder structure to exploit its deep nonlinear formulation. The extensive experimental results on six real-world datasets demonstrate that the proposed model achieves uniform superiority over the benchmark methods.

Heterogeneous Ensemble-Based Spike-Driven Few-Shot Online Learning

Spiking neural networks (SNNs) are regarded as a promising candidate to deal with the major challenges of current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the few-shot learning performance of artificial neural networks. Importantly, existing spike-based few-shot learning models do not target robust learning based on spatiotemporal dynamics and superior machine learning theory. In this paper, we propose a novel spike-based framework with the entropy theory, namely, heterogeneous ensemble-based spike-driven few-shot online learning (HESFOL). The proposed HESFOL model uses the entropy theory to establish the gradient-based few-shot learning scheme in a recurrent SNN architecture. We examine the performance of the HESFOL model based on the few-shot classification tasks using spiking patterns and the Omniglot data set, as well as the few-shot motor control task using an end-effector. Experimental results show that the proposed HESFOL scheme can effectively improve the accuracy and robustness of spike-driven few-shot learning performance. More importantly, the proposed HESFOL model emphasizes the application of modern entropy-based machine learning methods in state-of-the-art spike-driven learning algorithms. Therefore, our study provides new perspectives for further integration of advanced entropy theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems.

Efficient correntropy-based multi-view clustering with anchor graph embedding

Although multi-view clustering has received widespread attention due to its far superior performance to single-view clustering, it still faces the following issues: (1) high computational cost, considering the introduction of multi-view information, reduces the clustering efficiency greatly; (2) complex noises and outliers, existed in real-world data, pose a huge challenge to the robustness of clustering algorithms. Currently, how to increase the efficiency and robustness has become two important issues of multi-view clustering. To cope with the above issues, an efficient correntropy-based multi-view clustering algorithm (ECMC) is proposed in this paper, which can not only improve clustering efficiency by constructing embedded anchor graph and utilizing nonnegative matrix factorization (NMF), but also enhance the robustness by exploring correntropy to suppress various noises and outliers. To further improve clustering efficiency, one of the factors of NMF is constrained to be an indicator matrix instead of a traditional non-negative matrix, so that the categories of samples can be obtained directly without any extra operation. Subsequently, a novel half-quadratic-based strategy is proposed to optimize the non-convex objective function of ECMC. Finally, extensive experiments on eight real-world datasets and eighteen noisy datasets show that ECMC can guarantee faster speed and better robustness than other state-of-the-art multi-view clustering algorithms.

Smoothness Regularized Multiview Subspace Clustering With Kernel Learning

Multiview subspace clustering has attracted an increasing amount of attention in recent years. However, most of the existing multiview subspace clustering methods assume linear relations between multiview data points when learning the affinity representation by means of the self-expression or fail to preserve the locality property of the original feature space in the learned affinity representation. To address the above issues, in this article, we propose a new multiview subspace clustering method termed smoothness regularized multiview subspace clustering with kernel learning (SMSCK). To capture the nonlinear relations between multiview data points, the proposed model maps the concatenated multiview observations into a high-dimensional kernel space, in which the linear relations reflect the nonlinear relations between multiview data points in the original space. In addition, to explicitly preserve the locality property of the original feature space in the learned affinity representation, the smoothness regularization is deployed in the subspace learning in the kernel space. Theoretical analysis has been provided to ensure that the optimal solution of the proposed model meets the grouping effect. The unique optimal solution of the proposed model can be obtained by an optimization strategy and the theoretical convergence analysis is also conducted. Extensive experiments are conducted on both image and document data sets, and the comparison results with state-of-the-art methods demonstrate the effectiveness of our method.