Abstract: As an unsupervised learning method, clustering is a significant research topic in data science. K-means is a partition-based clustering algorithm, which generally uses a heuristic algorithm to solve a discrete NP problem. In order to improve the application of K-means in big data problems, a continuous non-convex K-means equivalent clustering model is designed according to the properties of clustering matrix, and the  fast optimization algorithm of this equivalent clustering medel is given by ADMM framework. Numerical experiments show that the model and algorithm are accurate and efficient in big data clustering. In addition, the feature and equivalence of the model are discussed.

Key words: K-means, clustering, sparse, alternating direction method of multipliers