In many real applications of machine learning and data mining, we are often confronted with high-dimensional data. How to cluster high-dimensional data is still a challenging problem due to the curse of dimensionality. In this paper, we try to address this problem using joint dimensionality reduction and clustering. Different from traditional approaches that conduct dimensionality reduction and clustering in sequence, we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively. Within this framework, we are able not only to view several traditional approaches and reveal their intrinsic relationships, but also to be stimulated to develop a new method. We also propose an effective approach for solving the formulated nonconvex optimization problem. Comprehensive analyses, including convergence behavior, parameter determination, and computational complexity, together with the relationship to other related approaches, are also presented. Plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state-of-the-art clustering approaches and existing joint dimensionality reduction and clustering methods.