Multilayer Graph Approach to Deep Subspace Clustering

Deep subspace clustering (DSC) networks based on self-expressive model learn representation matrix, often implemented in terms of fully connected network, in the embedded space. After the learning is finished, representation matrix is used by spectral clustering module to assign labels to clusters. However, such approach ignores complementary information that exist in other layers of the encoder (including the input data themselves). Herein, we apply selected linear subspace clustering algorithm to learn representation matrices from representations learned by all layers of encoder network including the input data. Afterward, we learn a multilayer graph that in a multi-view like manner integrates information from graph Laplacians of all used layers. That improves further performance of selected DSC network. Furthermore, we also provide formulation of our approach to cluster out-of-sample/test data points. We validate proposed approach on four well-known datasets with two DSC networks as baseline models. In almost all the cases, proposed approach achieved statistically significant improvement in three performance metrics. MATLAB code of proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.

Adaptively Topological Tensor Network for Multi-view Subspace Clustering

Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined tensor decomposition may not fully exploit low rank information for a certain dataset, resulting in sub-optimal multi-view clustering performance. To alleviate the aforementioned limitations, we propose the adaptively topological tensor network (ATTN) by determining the edge ranks from the structural information of the self-representation tensor, and it can give a better tensor representation with the data-driven strategy. Specifically, in multi-view tensor clustering, we analyze the higher-order correlations among different modes of a self-representation tensor, and prune the links of the weakly correlated ones from a fully connected tensor network. Therefore, the newly obtained tensor networks can efficiently explore the essential clustering information with self-representation with different tensor structures for various datasets. A greedy adaptive rank-increasing strategy is further applied to improve the capture capacity of low rank structure. We apply ATTN on multi-view subspace clustering and utilize the alternating direction method of multipliers to solve it. Experimental results show that multi-view subspace clustering based on ATTN outperforms the counterparts on six multi-view datasets.

Deep Multi-View Subspace Clustering with Anchor Graph

Deep multi-view subspace clustering (DMVSC) has recently attracted increasing attention due to its promising performance. However, existing DMVSC methods still have two issues: (1) they mainly focus on using autoencoders to nonlinearly embed the data, while the embedding may be suboptimal for clustering because the clustering objective is rarely considered in autoencoders, and (2) existing methods typically have a quadratic or even cubic complexity, which makes it challenging to deal with large-scale data. To address these issues, in this paper we propose a novel deep multi-view subspace clustering method with anchor graph (DMCAG). To be specific, DMCAG firstly learns the embedded features for each view independently, which are used to obtain the subspace representations. To significantly reduce the complexity, we construct an anchor graph with small size for each view. Then, spectral clustering is performed on an integrated anchor graph to obtain pseudo-labels. To overcome the negative impact caused by suboptimal embedded features, we use pseudo-labels to refine the embedding process to make it more suitable for the clustering task. Pseudo-labels and embedded features are updated alternately. Furthermore, we design a strategy to keep the consistency of the labels based on contrastive learning to enhance the clustering performance. Empirical studies on real-world datasets show that our method achieves superior clustering performance over other state-of-the-art methods.

Multi-view MERA Subspace Clustering

Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing to fully explore inter/intra-view information. Using the advanced tensor network, namely, multi-scale entanglement renormalization ansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where MERA factorizes a tensor into contractions of one top core factor and the rest orthogonal/semi-orthogonal factors. Benefiting from multiple interactions among orthogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong representation power to capture the complex inter/intra-view information in the self-representation tensor. The alternating direction method of multipliers is adopted to solve the optimization model. Experimental results on five multi-view datasets demonstrate MERA-MSC has superiority against the compared algorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by incorporating anchor learning to develop a scalable low-rank MERA based multi-view clustering method (sMREA-MVC). The effectiveness and efficiency of sMERA-MVC have been validated on three large-scale multi-view datasets. To our knowledge, this is the first work to introduce MERA to the multi-view clustering topic. The codes of MERA-MSC and sMERA-MVC are publicly available at https://github.com/longzhen520/MERA-MSC.

Towards Generalized Multi-stage Clustering: Multi-view Self-distillation

Existing multi-stage clustering methods independently learn the salient features from multiple views and then perform the clustering task. Particularly, multi-view clustering (MVC) has attracted a lot of attention in multi-view or multi-modal scenarios. MVC aims at exploring common semantics and pseudo-labels from multiple views and clustering in a self-supervised manner. However, limited by noisy data and inadequate feature learning, such a clustering paradigm generates overconfident pseudo-labels that mis-guide the model to produce inaccurate predictions. Therefore, it is desirable to have a method that can correct this pseudo-label mistraction in multi-stage clustering to avoid the bias accumulation. To alleviate the effect of overconfident pseudo-labels and improve the generalization ability of the model, this paper proposes a novel multi-stage deep MVC framework where multi-view self-distillation (DistilMVC) is introduced to distill dark knowledge of label distribution. Specifically, in the feature subspace at different hierarchies, we explore the common semantics of multiple views through contrastive learning and obtain pseudo-labels by maximizing the mutual information between views. Additionally, a teacher network is responsible for distilling pseudo-labels into dark knowledge, supervising the student network and improving its predictive capabilities to enhance the robustness. Extensive experiments on real-world multi-view datasets show that our method has better clustering performance than state-of-the-art methods.

Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor Space for Multi-view Clustering

Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations and improving clustering analysis of multi-view data. Nevertheless, most of existing investigations are typically hampered by the two flaws. First, self-representation based tensor subspace learning usually induces high time and space complexity, and is limited in perceiving nonlinear local structure in the embedding space. Second, the tensor singular value decomposition (t-SVD) model redistributes each singular value equally without considering the diverse importance among them. To well cope with the issues, we propose a hyper-Laplacian regularized concept factorization (HLRCF) in low-rank tensor space for multi-view clustering. Specifically, we adopt the concept factorization to explore the latent cluster-wise representation of each view. Further, the hypergraph Laplacian regularization endows the model with the capability of extracting the nonlinear local structures in the latent space. Considering that different tensor singular values associate structural information with unequal importance, we develop a self-weighted tensor Schatten p-norm to constrain the tensor comprised of all cluster-wise representations. Notably, the tensor with smaller size greatly decreases the time and space complexity in the low-rank optimization. Finally, experimental results on eight benchmark datasets exhibit that HLRCF outperforms other multi-view methods, showingcasing its superior performance.

Double Graphs Regularized Multi-view Subspace Clustering

Recent years have witnessed a growing academic interest in multi-view subspace clustering. In this paper, we propose a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method, which aims to harness both global and local structural information of multi-view data in a unified framework. Specifically, DGRMSC firstly learns a latent representation to exploit the global complementary information of multiple views. Based on the learned latent representation, we learn a self-representation to explore its global cluster structure. Further, Double Graphs Regularization (DGR) is performed on both latent representation and self-representation to take advantage of their local manifold structures simultaneously. Then, we design an iterative algorithm to solve the optimization problem effectively. Extensive experimental results on real-world datasets demonstrate the effectiveness of the proposed method.

Preventing Dimensional Collapse of Incomplete Multi-View Clustering via Direct Contrastive Learning

Incomplete multi-view clustering (IMVC) is an unsupervised approach, among which IMVC via contrastive learning has received attention due to its excellent performance. The previous methods have the following problems: 1) Over-reliance on additional projection heads when solving the dimensional collapse problem in which latent features are only valid in lower-dimensional subspaces during clustering. However, many parameters in the projection heads are unnecessary. 2) The recovered view contain inconsistent private information and useless private information will mislead the learning of common semantics due to consistent learning and reconstruction learning on the same feature. To address the above issues, we propose a novel incomplete multi-view contrastive clustering framework. This framework directly optimizes the latent feature subspace, utilizes the learned feature vectors and their sub-vectors for reconstruction learning and consistency learning, thereby effectively avoiding dimensional collapse without relying on projection heads. Since reconstruction loss and contrastive loss are performed on different features, the adverse effect of useless private information is reduced. For the incomplete data, the missing information is recovered by the cross-view prediction mechanism and the inconsistent information from different views is discarded by the minimum conditional entropy to further avoid the influence of private information. Extensive experimental results of the method on 5 public datasets show that the method achieves state-of-the-art clustering results.

Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering

With powerful ability to exploit latent structure of self-representation information, different tensor decompositions have been employed into low rank multi-view clustering (LRMVC) models for achieving significant performance. However, current approaches suffer from a series of problems related to those tensor decomposition, such as the unbalanced matricization scheme, rotation sensitivity, deficient correlations capture and so forth. All these will lead to LRMVC having insufficient access to global information, which is contrary to the target of multi-view clustering. To alleviate these problems, we propose a new tensor decomposition called Tucker-O-Minus Decomposition (TOMD) for multi-view clustering. Specifically, based on the Tucker format, we additionally employ the O-minus structure, which consists of a circle with an efficient bridge linking two weekly correlated factors. In this way, the core tensor in Tucker format is replaced by the O-minus architecture with a more balanced structure, and the enhanced capacity of capturing the global low rank information will be achieved. The proposed TOMD also provides more compact and powerful representation abilities for the self-representation tensor, simultaneously. The alternating direction method of multipliers is used to solve the proposed model TOMD-MVC. Numerical experiments on six benchmark data sets demonstrate the superiority of our proposed method in terms of F-score, precision, recall, normalized mutual information, adjusted rand index, and accuracy.

Subspace-Contrastive Multi-View Clustering

Most multi-view clustering methods are limited by shallow models without sound nonlinear information perception capability, or fail to effectively exploit complementary information hidden in different views. To tackle these issues, we propose a novel Subspace-Contrastive Multi-View Clustering (SCMC) approach. Specifically, SCMC utilizes view-specific auto-encoders to map the original multi-view data into compact features perceiving its nonlinear structures. Considering the large semantic gap of data from different modalities, we employ subspace learning to unify the multi-view data into a joint semantic space, namely the embedded compact features are passed through multiple self-expression layers to learn the subspace representations, respectively. In order to enhance the discriminability and efficiently excavate the complementarity of various subspace representations, we use the contrastive strategy to maximize the similarity between positive pairs while differentiate negative pairs. Thus, a weighted fusion scheme is developed to initially learn a consistent affinity matrix. Furthermore, we employ the graph regularization to encode the local geometric structure within varying subspaces for further fine-tuning the appropriate affinities between instances. To demonstrate the effectiveness of the proposed model, we conduct a large number of comparative experiments on eight challenge datasets, the experimental results show that SCMC outperforms existing shallow and deep multi-view clustering methods.