Data perturbation aims to disguise original data values so the confidential information is kept safe and the disclosure risk is minimized. In this article, we exploit the characteristics of nonmetric multidimensional scaling (NMDS) to transform data and generate perturbed data. We hypothesize that NMDS is a good tool for privacy-preserving data clustering. For this, our model should preserve the distance between data objects (data utility in the context of clustering) whilst introducing enough uncertainty about the original data. We discuss privacy attacks in the context of disclosing the original data values and show that our method introduces uncertainty which could hinder the attacker from determining the exact location of points in the original space. We examine our model on a number of benchmark datasets and compare the results obtained from the perturbed data with those obtained from the original data using a number of clustering algorithms. We compare with other data perturbation techniques such as principal component analysis (PCA), random projection, single value decomposition and discrete cosine transform. We show that both NMDS and PCA produce the best utility preservation, obtaining clusterings of the perturbed data which are very similar to those on the original data. We also show that the transformation using NMDS introduces more uncertainty than other transformations in the point placement location and as the transformation is independent of the original data values it should produce enhanced privacy preservation.