Speaker : | Prof. Fushing Hsieh (UC Davis, University of California) |
Title : | Data Mechanics and coupling geometry on binary bipartite networks |
Time : | 2014-06-16 (Mon) 14:10 - 15:10 |
Place : | Seminar Room 617, Institute of Mathematics (NTU Campus) |
Abstract: | A binary bipartite network is taken as a thermodynamic system embracing all up-and-down spin configurations defined by product-permutations on rows and columns of a binary data matrix. This system is equipped with its ferromagnetic energy ground state under Ising model potential. A new computing paradigm for indirect searching for such a macrostate, called Data Mechanics, is devised by iteratively building a surrogate geometric system with a pair of nearly optimal marginal ultrametrics on row and column spaces. The coupling measure minimizing the Gromov-Wasserstein distance of these two marginal geometries is also seen to be in the vicinity of the macrostate. This resultant coupling geometry reveals multi-scale block pattern information that characterizes multiple layers of interacting relationships between clusters on row and on column axes. It is the nonparametric information content of a binary bipartite network. This coupling geometry is then demonstrated to shed new light and bring resolution to interaction issues in community ecology and in gene-content-based phylogenetics. Its implied global inferences are expected to have high potential in many scientific areas. |