  In data science, determining proximity between observations is critical to
many downstream analyses such as clustering, information retrieval and
classification. However, when the underlying structure of the data probability
space is unclear, the function used to compute similarity between data points
is often arbitrarily chosen. Here, we present a novel concept of proximity,
Semblance, that uses the empirical distribution across all observations to
inform the similarity between each pair. The advantage of Semblance lies in its
distribution free formulation and its ability to detect niche features by
placing greater emphasis on similarity between observation pairs that fall at
the outskirts of the data distribution, as opposed to those that fall towards
the center. We prove that Semblance is a valid Mercer kernel, thus allowing its
principled use in kernel based learning machines. Semblance can be applied to
any data modality, and we demonstrate its consistently improved performance
against conventional methods through simulations and three real case studies
from very different applications, viz. cell type classification using single
cell RNA sequencing, selecting predictors of positive return on real estate
investments, and image compression.
