An improved K-means algorithm based on persistent homology

The traditional K-means algorithm has several limitations, including sensitivity to initial center, unstable clustering results, local optimal clustering results, and a large number of iterations. In this paper, we propose an improved clustering algorithm called PH-K-means that utilizes the persistent homology to identify k clusters in the data set. The algorithm calculates the length of the longest Betti number to obtain k Betti numbers, which represent the k clusters respectively. The data is then output in k Betty numbers, and the average value of the data in each Betti number is used as the initialization center of k clusters. The algorithm iterates until the difference of the square sum of the errors in the adjacent two clusters is less than the threshold value. The PH-K-means algorithm is tested on seven common data sets, and the results show that it has high accuracy, stable clustering results, and requires fewer iterations than traditional K-means, K-means++, UK-means, and K-means algorithms.