Extensions of X-means with Efficient Learning the Number of Clusters
Gyeongyong Heo, Young-Woon Woo · The Journal of the Korean Institute of Information and Communication Engineering · 2008
K-means is one of the simplest unsupervised learning algorithms that solve the clustering problem. However K-means suffers the basic shortcoming: the number of clusters k has to be known in advance. In this paper, we propose extensions of X-means, which can estimate the number of clusters using Bayesian information criterion(BIC). We introduce two different versions of algorithm: modified X-means(MX-means) and generalized X-means(GX-means), which employ one full covariance matrix for one cluster and so can estimate the number of clusters efficiently without severe over-fitting which X-means suffers due to its spherical cluster assumption. The algorithms start with one cluster and try to split a cluster iteratively to maximize the BIC score. The former uses K-means algorithm to find a set of optimal clusters with current k, which makes it simple and fast. However it generates wrongly estimated centers when the clusters are overlapped. The latter uses EM algorithm to estimate the parameters and generates more stable clusters even when the clusters are overlapped. Experiments with synthetic data show that the purposed methods can provide a robust estimate of the number of clusters and cluster parameters compared to other existing top-down algorithms.