  Biomedical research often produces high-dimensional data confounded by batch
effects such as systematic experimental variations, different protocols and
subject identifiers. Without proper correction, low-dimensional representation
of high-dimensional data might encode and reproduce the same systematic
variations observed in the original data, and compromise the interpretation of
the results. In this article, we propose a novel procedure to remove batch
effects from low-dimensional embeddings obtained with t-SNE dimensionality
reduction. The proposed methods are based on linear algebra and constrained
optimization, leading to efficient algorithms and fast computation in many
high-dimensional settings. Results on artificial single-cell transcription
profiling data show that the proposed procedure successfully removes multiple
batch effects from t-SNE embeddings, while retaining fundamental information on
cell types. When applied to single-cell gene expression data to investigate
mouse medulloblastoma, the proposed method successfully removes batches related
with mice identifiers and the date of the experiment, while preserving clusters
of oligodendrocytes, astrocytes, and endothelial cells and microglia, which are
expected to lie in the stroma within or adjacent to the tumors.
