Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view (2102.07943v1)

Abstract: Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to unseen data points. In this work, we propose a scalable graph learning framework, seeking to address the above three challenges simultaneously. Specifically, it is based on the ideas of anchor points and bipartite graph. Rather than building a $n\times n$ graph, where $n$ is the number of samples, we construct a bipartite graph to depict the relationship between samples and anchor points. Meanwhile, a connectivity constraint is employed to ensure that the connected components indicate clusters directly. We further establish the connection between our method and the K-means clustering. Moreover, a model to process multi-view data is also proposed, which is linear scaled with respect to $n$. Extensive experiments demonstrate the efficiency and effectiveness of our approach with respect to many state-of-the-art clustering methods.

• The paper introduces a novel scalable approach by leveraging anchor points and bipartite graphs to construct structured graphs for subspace clustering.
• The paper imposes rank constraints on the Laplacian matrix to ensure a predefined number of connected components, linking the method to K-means clustering.
• Empirical results demonstrate improved clustering accuracy and efficiency, confirming robustness in both single-view and multi-view data scenarios.

Structured Graph Learning for Scalable Subspace Clustering

The paper "Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view" introduces an innovative approach to subspace clustering, addressing key challenges such as computational efficiency, cluster elucidation, and generalization to unseen data. This paper is pivotal for researchers aiming to advance clustering techniques within the realms of machine learning, pattern recognition, and data mining.

Graph-based subspace clustering has previously been hampered by issues including high computational costs, ambiguity in cluster definition, and limitations when dealing with new data points. Traditional methodologies like sparse subspace clustering (SSC) and low-rank representation (LRR) rely on constructing dense graphs, which are computationally expensive and may not scale well to large datasets. Moreover, these methods often treat clustering as a separate, subsequent process, which can result in suboptimal clustering outcomes.

The proposed framework leverages the concept of anchor points and bipartite graphs to construct a scalable clustering method. Instead of the traditional $n \times n$ graph construction, the method generates a bipartite graph portraying the relationship between samples and anchor points, substantially decreasing both computational time and memory usage. This approach not only guarantees the robustness of the clustering process by ensuring connected components represent explicit clusters, but it also ties in spectral graph theory concepts to maintain a structured graph representation.

A significant theoretical development in this paper is the connection it establishes between structured graph learning and K-means clustering. By imposing rank constraints on the Laplacian matrix, the method ensures the resultant bipartite graph contains a predefined number of connected components, corresponding directly to the required clusters. As a result, the algorithm demonstrates linear scaling in complexity with respect to the number of data samples, marking a significant improvement over traditional clustering methods that often exhibit cubic complexity.

To further address the limitations of single-view clustering, the paper extends the proposed model to handle multi-view data. In the multi-view scenario, integration across views is crucial due to varying data characteristics across different perspectives. The model incorporates view-wise weightings to differentiate the contributions of various views, enabling a more nuanced clustering process that can discern and integrate complementary information from multiple data streams.

Empirical evaluation highlights the competitive performance of the proposed method across several datasets, showcasing improvements in clustering accuracy and efficiency compared to state-of-the-art methods. The experiments confirm the method's scalability and its capability to manage large-scale data effectively, a testament to its practical applicability.

In sum, this paper offers significant contributions to the field of subspace clustering, presenting a novel structured graph learning framework that reconciles previous methods' shortcomings. The implications of this work are substantial, providing a framework that balances computational efficacy with accurate cluster representation, all while being extendable to multi-view contexts and adept at handling out-of-sample data efficiently.

Future work will likely focus on further optimizing anchor selection processes and enhancing the robustness of the clustering output through adaptive learning strategies, which could provide even more nuanced interpretations of complex, large-scale datasets. Furthermore, integrating this approach with emerging neural network architectures could yield powerful hybrid models capable of addressing even more diverse clustering challenges.