A Group-Theoretic Approach to Computational Abstraction: Symmetry-Driven Hierarchical Clustering
This work addresses the challenge of abstraction in concept learning and knowledge discovery for AI and cognitive science, offering a novel theoretical and algorithmic foundation, though it appears incremental in building on group theory and clustering concepts.
The paper tackled the problem of computational abstraction by proposing a symmetry-driven hierarchical clustering framework that is data-free, feature-free, similarity-free, and globally hierarchical, distinguishing it from traditional models like k-means, and illustrated its application in realizing Shannon's information lattice and enabling automatic concept learning.
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.