In this paper we address the problem of high-dimensionality for data that lies on complex manifolds. In high-dimensional spaces, distances between the nearest and farthest neighbour tend to become equal. This behaviour hardens data analysis, such as clustering. We show that distance transformation can be used in an effective way to obtain an embedding space of lower-dimensionality than the original space and that increases the quality of data analysis. The new method, called High-Dimensional Multimodal Embedding (HDME) is compared with known state-of-the-art methods operating in high-dimensional spaces and shown to be effective both in terms of retrieval and clustering on real world data.