  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.
