Multi-graph Fusion for Multi-view Spectral Clustering (1909.06940v1)

Abstract: A panoply of multi-view clustering algorithms has been developed to deal with prevalent multi-view data. Among them, spectral clustering-based methods have drawn much attention and demonstrated promising results recently. Despite progress, there are still two fundamental questions that stay unanswered to date. First, how to fuse different views into one graph. More often than not, the similarities between samples may be manifested differently by different views. Many existing algorithms either simply take the average of multiple views or just learn a common graph. These simple approaches fail to consider the flexible local manifold structures of all views. Hence, the rich heterogeneous information is not fully exploited. Second, how to learn the explicit cluster structure. Most existing methods don't pay attention to the quality of the graphs and perform graph learning and spectral clustering separately. Those unreliable graphs might lead to suboptimal clustering results. To fill these gaps, in this paper, we propose a novel multi-view spectral clustering model which performs graph fusion and spectral clustering simultaneously. The fusion graph approximates the original graph of each individual view but maintains an explicit cluster structure. Experiments on four widely used data sets confirm the superiority of the proposed method.

• The paper introduces GFSC, which concurrently fuses graphs and performs spectral clustering to capture both global and local data structures.
• It overcomes limitations of traditional averaging methods by dynamically weighting individual views to mitigate the impact of noise.
• Empirical results on datasets like BBC and Reuters demonstrate enhanced accuracy, normalized mutual information, and purity compared to conventional methods.

Overview of "Multi-graph Fusion for Multi-view Spectral Clustering"

The paper "Multi-graph Fusion for Multi-view Spectral Clustering" examines various techniques for improving clustering performance in multi-view data contexts by utilizing spectral clustering approaches. These methods focus on integrating multiple views of data to better capture underlying structures which are often missed by single-view clustering models. The proposed method, referred to as GFSC (Graph Fusion for Spectral Clustering), aims to address specific limitations of existing approaches, specifically targeting the challenge of graph fusion and the integration of explicit cluster dependencies within the spectral clustering process.

Key Contributions

The paper identifies two critical deficiencies in current multi-view spectral clustering approaches:

1. Graph Fusion Challenges: Traditional methods usually simplify graph fusion by averaging or learning a single common graph among various views. Such strategies often fail to acknowledge distinct local manifold structures, leading to suboptimal exploitation of multi-view data.
2. Explicit Cluster Learning: Many existing techniques operate under separate graph learning and clustering stages, which can compromise graph quality and, by extension, the final clustering outcomes.

In response, the paper proposes a unified model that concurrently performs graph fusion alongside spectral clustering. The new method maintains a fusion graph that approximates original graphs from each individual view while preserving an explicit cluster structure. The algorithm's architecture encourages interaction between graph learning processes and clustering tasks, enhancing both accuracy and computational efficiency.

Technical Summary

The GFSC approach uniquely constructs graphs for each view based on a self-expressiveness property, facilitating robust capturing of global structure encoded by data correlations. The novelty of GFSC arises from its dynamic weighting scheme in graph fusion, which assigns importance to views based on relative contributions, effectively mitigates the negative impact of noise-laden views. Additionally, the incorporation of cluster structure learning optimizes the consensus graph by ensuring it retains exactly k connected components, where k denotes the number of clusters.

Iterative Optimization:

• The algorithm utilizes an iterative approach to solve the optimization problem, alternating between updating graph weights, fusing graphs, and refining cluster structures.
• Weight parameters are refined using an inverse distance weighting scheme, dynamically prioritizing views with graphs closer to an optimal consensus graph.

Empirical Results

Extensive experiments conducted on datasets like BBC, Reuters, Digits, and Caltech20 demonstrate the superior clustering performance of the GFSC model compared to traditional methods. Specifically, metrics including accuracy, normalized mutual information, and purity indicate significant improvements over both multi-view spectral and K-means clustering counterparts. GFSC consistently surpasses methods like Co-training, Co-regularization, Multi-view Kernel K-means, and others, showcasing its adeptness in leveraging diverse view information.

Implications and Future Directions

The findings have immediate implications for applications relying on multi-view data such as computer vision, bioinformatics, and natural language processing. Practitioners can benefit from integrating GFSC into existing workflows to enhance data-driven insights and outcomes. Theoretically, this work lays the groundwork for more sophisticated models that could explore alternative metrics or inclusion of deep learning techniques to further marry graph learning with spectral clustering adaptability.

Looking forward, research could expand on the real-time adaptability of the GFSC algorithm, especially in dynamic environments with streaming data. Exploring hybrid models that integrate machine learning paradigms could provide additional robustness and precision in discovering latent multi-view structures.