  We introduce Uniform Manifold Approximation with Two-phase Optimization
(UMATO), a dimensionality reduction (DR) technique that improves UMAP to
capture the global structure of high-dimensional data more accurately. In
UMATO, optimization is divided into two phases so that the resulting embeddings
can depict the global structure reliably while preserving the local structure
with sufficient accuracy. In the first phase, hub points are identified and
projected to construct a skeletal layout for the global structure. In the
second phase, the remaining points are added to the embedding preserving the
regional characteristics of local areas. Through quantitative experiments, we
found that UMATO (1) outperformed widely used DR techniques in preserving the
global structure while (2) producing competitive accuracy in representing the
local structure. We also verified that UMATO is preferable in terms of
robustness over diverse initialization methods, number of epochs, and
subsampling techniques.
