This paper proposes a new representation space, called the cluster space, for data points that originate from high dimensions. Whereas existing dedicated methods concentrate on revealing manifolds from within the data, we consider here the context of clustered data and derive the dimension reduction process from cluster information. Points are represented in the cluster space by means of their a posteriori probability values estimated using Gaussian Mixture Models. The cluster space obtained is the optimal space for discrimination in terms of the Quadratic Discriminant Analysis (QDA).Moreover, it is shown to alleviate the negative impact of the curse of dimensionality on the quality of cluster discrimination and is a useful preprocessing tool for other dimension reduction methods. Various experiments illustrate the effectiveness of the cluster space bothon synthetic and real data.