VODC method

Voronoi Diagram Clustering (VODC) Method

Voronoi diagram clustering (VODC) is a method of grouping data points into clusters that is relatively efficient and straightforward. First proposed by Ang and Shao (2011), VODC is an iterative refinement method for cluster analysis that is based on the Voronoi diagram, balancing the Voronoi cell edge lengths with the cluster number and the average intra-cluster distance.

A Voronoi diagram is made up of a set of polygons (cells) that are bordered by a set of lines. Each cell surrounds a point (or cluster) and is composed of all the points that are closer to a single point than any other point. This makes Voronoi diagrams a powerful tool for cluster analysis.

The VODC method works by computing the Voronoi cells of a set of points in a given dataset. It then uses the quality of the cells to define the clusters needed to best represent the dataset.

The first stage of the VODC method is the identification of the initial set of Voronoi cells. This is done by randomly sampling the dataset and computing the Voronoi cells for those points. A Voronoi cell is then assigned to each sampled point. The quality of the cells is then evaluated by computing the area of the polygons, the relative edge length, and the average intramural distance; that is, the distance between the centroid of each Voronoi cell and its neighbouring cells.

Once the quality of the Voronoi cells is evaluated, the clustering process begins. The points inside each Voronoi cell are grouped into the respective cluster and a least squares fit is then applied to each cluster to remove outliers. This is done to ensure that the dataset is representative of the original clusters.

The Voronoi cells are then re-computed and, if needed, clusters may be added or removed depending on the quality of the cells and the dataset. This process is repeated until the optimal number of clusters has been determined.

The VODC method is also sensitive to different types of noise and is able to flag and remove noises points automatically. This helps to improve the accuracy of the clusters produced by the method. In addition, the VODC method is able to identify different types of clusters (e.g. hard and fuzzy clusters) and can be used on datasets of different sizes and dimensions.

Overall, the Voronoi diagram clustering method is a powerful tool for cluster analysis and provides a relatively straightforward and efficient approach for grouping datasets. It is a useful method for tackling different types of datasets and can be used for various applications.