The ability to cluster high-dimensional categorical data is essential for many machine learning applications such as bioinfomatics. Currently, central clustering of categorical data is a difficult problem due to the lack of a geometrically interpretable definition of a cluster center. In this paper, we propose a novel kernel-density-based definition using a Bayes-type probability estimator. Then, a new algorithm called k-centers is proposed for central clustering of categorical data, incorporating a new feature weighting scheme by which each attribute is automatically assigned with a weight measuring its individual contribution for the clusters. Experimental results on real-world data show outstanding performance of the proposed algorithm, especially in recognizing the biological patterns in DNA sequences.