Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure. They are known to group data points at the same time as they embed them, resulting in visualizations with well-separated clusters that preserve local information well. However, t-SNE and UMAP also tend to distort the global geometry of the underlying data. We propose a more transparent modular approach that first clusters the data, then embeds each cluster, and finally aligns the clusters to obtain a global embedding. We demonstrate this approach on several synthetic and real-world datasets and show that it is competitive with existing methods, while being much more transparent.

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