  Abstraction plays a key role in concept learning and knowledge discovery;
this paper is concerned with computational abstraction. In particular, we study
the nature of abstraction through a group-theoretic approach, formalizing it as
symmetry-driven---as opposed to data-driven---hierarchical clustering. Thus,
the resulting clustering framework is data-free, feature-free, similarity-free,
and globally hierarchical---the four key features that distinguish it from
common data clustering models such as $k$-means. Beyond a theoretical
foundation for abstraction, we also present a top-down and a bottom-up approach
to establish an algorithmic foundation for practical abstraction-generating
methods. Lastly, via both a theoretical explanation and a real-world
application, we illustrate that further coupling of our abstraction framework
with statistics realizes Shannon's information lattice and even further, brings
learning into the picture. This not only presents one use case of our proposed
computational abstraction, but also gives a first step towards a principled and
cognitive way of automatic concept learning and knowledge discovery.
