A Fixed point view: A Model-Based Clustering Framework
This provides a foundational framework for clustering algorithms, potentially aiding future design, but it is incremental as it builds on existing model-based approaches without demonstrating broad SOTA gains.
The paper tackles the lack of a unified mathematical framework for clustering analysis by proposing a fixed-point-based model that restates model-based clustering and reveals convergence mechanisms and interconnections among algorithms, with Gaussian mixture models (GMM) mapped as an application.
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering and proposes a unified clustering framework. In order to find fixed points as cluster centers, the framework iteratively constructs the contraction map, which strongly reveals the convergence mechanism and interconnections among algorithms. By specifying a contraction map, Gaussian mixture model (GMM) can be mapped to the framework as an application. We hope the fixed point framework will help the design of future clustering algorithms.