  Dimension reduction (DR) methods provide systematic approaches for analyzing
high-dimensional data. A key requirement for DR is to incorporate global
dependencies among original and embedded samples while preserving clusters in
the embedding space. To achieve this, we combine the principles of optimal
transport (OT) and principal component analysis (PCA). Our method seeks the
best linear subspace that minimizes reconstruction error using entropic OT,
which naturally encodes the neighborhood information of the samples. From an
algorithmic standpoint, we propose an efficient block-majorization-minimization
solver over the Stiefel manifold. Our experimental results demonstrate that our
approach can effectively preserve high-dimensional clusters, leading to more
interpretable and effective embeddings. Python code of the algorithms and
experiments is available online.
