Farthest boundary clustering algorithm: Half-orbital extreme pole

Clustering analysis is a process of splitting a dataset into various groups of smaller datasets such that instances in a particular group are more similar to one another than instances from other groups. In this paper, we propose a novel boundary approach to perform a clustering analysis. Our algorithm starts from identifying two instances that have the largest distance within the dataset, called extreme poles. The two farthest pairs of instances can either be two far ends of the same cluster group or two far ends of two different groups. Then a vector core is generated using these two poles. Various pre-determined distances from one of these two poles will split data into various layers. If the extreme poles lie within one group, then the number of instances within the layers must be distributed appropriately. Otherwise, the dataset needs to be split. Our algorithm will recursively perform on these smaller datasets until the stopping criteria are met. To demonstrate the effectiveness of our method, we compare our algorithm with the K-means clustering algorithm using the value of K from our algorithm. The results show that the total variance from our algorithm is not larger than that from the K-means algorithm.