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Dimension reduction tools preserving similarity and graph structure such as t-SNE and UMAP can capture complex biological patterns in high-dimensional data. However, these tools typically are not designed to separate effects of interest from unwanted effects due to confounders. We introduce the partial embedding (PARE) framework, which enables removal of confounders from any distance-based dimension reduction method. We then develop partial t-SNE and partial UMAP and apply these methods to genomic and neuroimaging data. For lower-dimensional visualization, our results show that the PARE framework can remove batch effects in single-cell sequencing data as well as separate clinical and technical variability in neuroimaging measures. We demonstrate that the PARE framework extends dimension reduction methods to highlight biological patterns of interest while effectively removing confounding effects.