Iterative Views Agreement: An Iterative Low-Rank based Structured Optimization Method to Multi-View Spectral Clustering (1608.05560v1)

Abstract: Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intuitiveness and robustness to noise corruptions. However, it aggressively tries to learn a common low-dimensional subspace for multi-view data, while inattentively ignoring the local manifold structure in each view, which is critically important to the spectral clustering; worse still, the low-rank minimization is enforced to achieve the data correlation consensus among all views, failing to flexibly preserve the local manifold structure for each view. In this paper, 1) we propose a multi-graph laplacian regularized LRR with each graph laplacian corresponding to one view to characterize its local manifold structure. 2) Instead of directly enforcing the low-rank minimization among all views for correlation consensus, we separately impose low-rank constraint on each view, coupled with a mutual structural consensus constraint, where it is able to not only well preserve the local manifold structure but also serve as a constraint for that from other views, which iteratively makes the views more agreeable. Extensive experiments on real-world multi-view data sets demonstrate its superiority.

Iterative Low-Rank Optimization for Multi-View Spectral Clustering

The paper "Iterative Views Agreement: An Iterative Low-Rank based Structured Optimization Method to Multi-View Spectral Clustering" introduces a novel framework designed to enhance multi-view spectral clustering. The authors focus on addressing significant shortcomings observed in conventional methodologies that attempt to extract a common low-dimensional subspace for multi-view data. This traditional approach often fails to adequately preserve local manifold structures, a critical aspect of effective spectral clustering.

In their methodological advance, the authors propose leveraging a low-rank representation refined with multi-graph Laplacian regularization. This innovative approach allows each graph Laplacian to represent the local manifold structure inherent in each view, rather than enforcing a singular subspace across all views. Furthermore, the introduction of a mutual structural consensus constraint allows each view to iteratively converge toward an agreeable representation by considering the manifold structure from both intra-view and inter-view perspectives.

Key Contributions

1. Multi-Graph Regularization: Instead of relying solely on a single low-dimensional subspace, the authors incorporate multi-graph Laplacian regularization. This inclusion allows for a more nuanced modeling of the nonlinear spectral graph structures, which are otherwise overlooked when focusing on achieving a consensus data representation.
2. Iterative View Agreement Process: The framework provides an iterative process for achieving view agreement. Each view's low-rank representation serves to regulate the learning process of other views. This mutual regulatory mechanism ensures that over successive iterations, the manifold structures become increasingly conformant, thus improving the consensus across all views.
3. Robustness to Noise: By separately imposing low-rank constraints on each view, the framework is inherently resistant to noise. This distinct capability is particularly necessary in realistic scenarios where data imperfections are common.

Experimental Evaluation

Empirical results demonstrate the superiority of the proposed framework across several real-world datasets, including the UCI digit dataset, the Animal with Attributes (AwA) dataset, and the NUS-WIDE-Object dataset. The authors reported substantial improvements in clustering accuracy (\textsf{ACC}) and normalized mutual information (\textsf{NMI}) over existing methods, including co-regularization techniques and other LRR-based models.

A critical observation is the enhanced performance achieved through the adaptive incorporation of view-specific manifold structures into the clustering process. The comprehensive experiments indicate that the proposed multi-graph regularization and iterative views agreement yield notable improvements, irrespective of feature noise and corruption.

Implications and Future Directions

The paper offers a significant methodological advancement for handling multi-view clustering tasks, particularly emphasizing the preservation of view-specific structures while achieving global clustering consensus. The implications of this work extend to numerous real-world applications where data is naturally multi-view and prone to noise, such as in image and document clustering tasks.

Future work, as suggested by the authors, might explore applying the iterative views agreement methodology beyond clustering to multi-modal data integration and cross-view learning paradigms. Developing such extensions could further improve cross-domain applications, including multi-modal information retrieval and collaborative filtering in heterogeneous networks.

In summary, this paper provides a sophisticated optimization framework for multi-view spectral clustering, capable of balancing the global requirement for consensus with local structural integrities. This scholarly contribution not only advances the theoretical understanding of multi-view data analysis but also enhances practical clustering performance in diverse applications.