機率研討會
主講者: 謝復興 教授 (UC Davis, University of California)
講題: Data Mechanics and coupling geometry on binary bipartite networks
時間: 2014-06-16 (Mon.)  14:10 - 15:10
地點: 數學所 617 研討室 (台大院區)
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.
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