arXiv 0809.04922008-09-02stat.MLstat.AP

From Data to the p-Adic or Ultrametric Model

Fionn Murtagh

备注：: 15 pages, 6 figures. To appear in: Proceedings of Third International Conference on p-Adic Mathematical Physics: From Planck Scale Physics to Complex Systems to Biology, Steklov Mathematics Institute, Russian Academy of Sciences
发表信息：: p-Adic Numbers, Ultrametric Analysis and Applications, 1, 58-68, 2009
DOI：: 10.1134/S2070046609010063

英文摘要：

We model anomaly and change in data by embedding the data in an ultrametric space. Taking our initial data as cross-tabulation counts (or other input data formats), Correspondence Analysis allows us to endow the information space with a Euclidean metric. We then model anomaly or change by an induced ultrametric. The induced ultrametric that we are particularly interested in takes a sequential - e.g. temporal - ordering of the data into account. We apply this work to the flow of narrative expressed in the film script of the Casablanca movie; and to the evolution between 1988 and 2004 of the Colombian social conflict and violence.

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