Deeper understanding on the geometrical and operational meaning of sparsity and entropy

Sparsity is a central notion in modern sensing, pattern recognition and communications systems, which aim to exploit the compact representations of underlying real-world phenomena. In the past hundred years, the measures to compute sparsity, traditionally in the form of entropy, have been characterized and qualified from the physical or operational, and information theoretic perspectives.

In this paper, instead, a classical mathematical approach using equivalence relations has enabled a minimal characterization of sparsity. This work introduced and demonstrated the generalized convexity nature of sparsity. Furthermore, the proposed entropy is a sub-linear time algorithm enabling large datasets analysis.

This research by Giancarlo Pastor Figueroa, a Postdoctoral Researcher in the mc2 – Mobile Cloud Computing group , has been recently accepted by the IEEE Transactions on Knowledge and Data Engineering.