Visualisation of high-dimensional data by means of a low-dimensional embedding plays a key role in explorative data analysis. Classical approaches to dimensionality reduction, such as principal component analysis (PCA) and multidimensional scaling (MDS), struggle or even fail to reveal the relevant data characteristics when applied to noisy or nonlinear data structures. We present a novel approach for dimensionality reduction in combination with an automatic noise cleaning. By employing self-organising agents that are governed by the dynamics of the superparamagnetic clustering algorithm, the method is able to generate denoised low-dimensional embeddings for which the characteristics of nonlinear data structures are preserved or even emphasised. These properties are illustrated and compared to other approaches by means of toy and real-world examples.