In pattern recognition and data mining, clustering is a classical technique to group matters of interest and has been widely employed to numerous applications. Among various clustering algorithms, K-means (KM) clustering is most popular for its simplicity and efficiency. However, with the rapid development of the social network, high-dimensional data are frequently generated, which poses a considerable challenge to the traditional KM clustering as the curse of dimensionality. In such scenarios, it is difficult to directly cluster such high-dimensional data that always contain redundant features and noises. Although the existing approaches try to solve this problem using joint subspace learning and KM clustering, there are still the following limitations: 1) the discriminative information in low-dimensional subspace is not well captured; 2) the intrinsic geometric information is seldom considered; and 3) the optimizing procedure of a discrete cluster indicator matrix is vulnerable to noises. In this paper, we propose a novel clustering model to cope with the above-mentioned challenges. Within the proposed model, discriminative information is adaptively explored by unifying local adaptive subspace learning and KM clustering. We extend the proposed model using a robust l2,1-norm loss function, where the robust cluster centroid can be calculated in a weighted iterative procedure. We also explore and discuss the relationships between the proposed algorithm and several related studies. Extensive experiments on kinds of benchmark data sets demonstrate the advantage of the proposed model compared with the state-of-the-art clustering approaches.