Graph Degree Linkage: Agglomerative Clustering on a Directed Graph (1208.5092v1)

Abstract: This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of clustering. The average indegree reflects the density near a sample, and the average outdegree characterizes the local geometry around a sample. Based on such insights, we define the affinity measure of clusters via the product of average indegree and average outdegree. The product-based affinity makes our algorithm robust to noise. The algorithm has three main advantages: good performance, easy implementation, and high computational efficiency. We test the algorithm on two fundamental computer vision problems: image clustering and object matching. Extensive experiments demonstrate that it outperforms the state-of-the-arts in both applications.

An Overview of Graph Degree Linkage for Agglomerative Clustering on Directed Graphs

The paper "Graph Degree Linkage: Agglomerative Clustering on a Directed Graph" introduces an innovative approach to clustering high-dimensional data through a graph-based agglomerative method. The proposed technique, known as Graph Degree Linkage (GDL), leverages fundamental graph theory concepts of indegree and outdegree to enhance clustering performance.

Methodology

The GDL algorithm distinguishes itself by utilizing directed graphs to represent data, building $K$-nearest-neighbor ($K$-NN) graphs from sample pairs to encapsulate the local manifold structures. Key to this approach is the definition of cluster affinity using the product of the average indegree and average outdegree. Indegree is indicative of the sample density, while outdegree characterizes the local geometry. This methodological choice provides robustness against noise, a common challenge in high-dimensional clustering tasks.

The algorithm follows the traditional agglomerative clustering framework, beginning with numerous small clusters that are iteratively merged based on maximum affinity. Importantly, the GDL computation efficiently leverages matrix operations, avoiding dependencies on complex numerical libraries, which enhances its computational efficiency.

Empirical Evaluation

The authors conduct thorough empirical evaluations, applying GDL to fundamental computer vision tasks such as image clustering and object matching. Across these applications, GDL demonstrates superior performance compared to several state-of-the-art clustering methods, including spectral clustering and affinity propagation. The algorithm shows particular resilience in handling varying densities and noisy datasets.

Performance is assessed across various image datasets, including COIL-20, COIL-100, MNIST, USPS, Extended Yale-B, and FRGC ver2.0, using NMI and CE as evaluation metrics. Results consistently indicate GDL's ability to outperform other methods in terms of clustering accuracy. Furthermore, despite its robustness, GDL remains computationally efficient, scaling linearly with the number of samples.

Implications and Future Work

The theoretical implications of GDL extend to the potential for enhancing clustering in tasks necessitating noise resistance and handling high-dimensionality. This approach may influence future work in fields where data representation in manifold spaces is pertinent. From a practical perspective, applications could extend beyond computer vision to domains like social network analysis and bioinformatics, where data often inherently forms complex networks.

For future research, exploring adaptive mechanisms for $K$-selection and testing across broader domain-specific datasets could provide further insight into robustness and versatility. Additionally, integrating GDL with other clustering paradigms could yield hybrid models that exploit the strengths of multiple approaches.

In conclusion, the paper provides evidence of GDL's capacity to effectively and efficiently tackle clustering on complex data structures, offering a new perspective on leveraging graph-theoretical principles in machine learning contexts.