  We propose a new embedding method, named Quantile-Quantile Embedding (QQE),
for distribution transformation and manifold embedding with the ability to
choose the embedding distribution. QQE, which uses the concept of
quantile-quantile plot from visual statistical tests, can transform the
distribution of data to any theoretical desired distribution or empirical
reference sample. Moreover, QQE gives the user a choice of embedding
distribution in embedding the manifold of data into the low dimensional
embedding space. It can also be used for modifying the embedding distribution
of other dimensionality reduction methods, such as PCA, t-SNE, and deep metric
learning, for better representation or visualization of data. We propose QQE in
both unsupervised and supervised forms. QQE can also transform a distribution
to either an exact reference distribution or its shape. We show that QQE allows
for better discrimination of classes in some cases. Our experiments on
different synthetic and image datasets show the effectiveness of the proposed
embedding method.
