Geometric visualization of clusters obtained from fuzzy clustering algorithms

Fuzzy-clustering methods, such as fuzzy k-means and expectation maximization, allow an object to be assigned to multiple clusters with different degrees of membership. However, the memberships that result from fuzzy-clustering algorithms are difficult to be analyzed and visualized. The memberships, usually converted to 0–1 values, are visualized using parallel coordinates or different color shades. In this paper, we propose a new approach to visualize fuzzy-clustered data. The scheme is based on a geometric visualization, and works by grouping the objects with similar cluster memberships towards the vertices of a hyper-tetrahedron. The proposed method shows clear advantages over the existing methods, demonstrating its capabilities for viewing and navigating inter-cluster relationships in a spatial manner.