  $t$-SNE is an embedding method that the data science community has widely Two
interesting characteristics of t-SNE are the structure preservation property
and the answer to the crowding problem, where all neighbors in high dimensional
space cannot be represented correctly in low dimensional space. $t$-SNE
preserves the local neighborhood, and similar items are nicely spaced by
adjusting to the local density. These two characteristics produce a meaningful
representation, where the cluster area is proportional to its size in number,
and relationships between clusters are materialized by closeness on the
embedding.
  This algorithm is non-parametric, therefore two initializations of the
algorithm would lead to two different embedding. In a forensic approach,
analysts would like to compare two or more datasets using their embedding. An
approach would be to learn a parametric model over an embedding built with a
subset of data. While this approach is highly scalable, points could be mapped
at the same exact position, making them indistinguishable. This type of model
would be unable to adapt to new outliers nor concept drift.
  This paper presents a methodology to reuse an embedding to create a new one,
where cluster positions are preserved. The optimization process minimizes two
costs, one relative to the embedding shape and the second relative to the
support embedding' match. The proposed algorithm has the same complexity than
the original $t$-SNE to embed new items, and a lower one when considering the
embedding of a dataset sliced into sub-pieces. The method showed promising
results on a real-world dataset, allowing to observe the birth, evolution and
death of clusters. The proposed approach facilitates identifying significant
trends and changes, which empowers the monitoring high dimensional datasets'
dynamics.
