  Dimensionality reduction (DR) on the manifold includes effective methods
which project the data from an implicit relational space onto a vectorial
space. Regardless of the achievements in this area, these algorithms suffer
from the lack of interpretation of the projection dimensions. Therefore, it is
often difficult to explain the physical meaning behind the embedding
dimensions. In this research, we propose the interpretable kernel DR algorithm
(I-KDR) as a new algorithm which maps the data from the feature space to a
lower dimensional space where the classes are more condensed with less
overlapping. Besides, the algorithm creates the dimensions upon local
contributions of the data samples, which makes it easier to interpret them by
class labels. Additionally, we efficiently fuse the DR with feature selection
task to select the most relevant features of the original space to the
discriminative objective. Based on the empirical evidence, I-KDR provides
better interpretations for embedding dimensions as well as higher
discriminative performance in the embedded space compared to the
state-of-the-art and popular DR algorithms.
