TWC Topological Weighted Centroid (Semeion©)
We can define as Topological Weighted Centroid (TWC) of N entities in a bi-dimensional space the centre of mass of these entities, weighted by the proximity of each entity to the others. The TWC represents the point where the entropy is minimal, so it is the point from which (if you were to put yourself there) other points generate maximum information.
An example of Escherichia Coli epidemics in Germany in 2011:
Source Data
TWC(Alpha): the outbreak
TWC(Beta): the time of the data collection
The TWC(Gamma): the next propagation
The Non Linear MST
References:
1)P.M. Buscema, E. Grossi, M. Breda, T. Jefferson, “Outbreaks source: A new mathematical approach to identify their possible location“, in Physica A 388 (2009) 47364762.
2)P.M. Buscema, M.Breda, L. Catzola, “The Topological Weighted Centroid, and the Semantic of the Physical Space – Theory“, in P.M.Buscema & E.Grossi (eds), Artificial Adaptive Systems in Medicine, 69-78, Bentham e-book,2009.
3) E. Grossi, P.M. Buscema, T. Jefferson, “The Topological Weighted Centroid and the Semantic of the Physical Space – Application“, in P.M. Buscema & E. Grossi (eds), Artificial Adaptive Systems in Medicine, 79-89, Bentham e-book,2009.
4)P.M. Buscema, M. Breda, E. Grossi, L. Catzola, P. L. Sacco, Semantics of Point Spaces Through the Topological Weighted Centroid and Other Mathematical Quantities: Theory and Applications, Chapter 4, pp 75-139, in W.J. Tastle (ed.), Data Mining Applications Using Artificial Adaptive Systems, DOI 10.1007/978-1-4614-4223-3_4, # Springer Science+Business Media New York 2013.
5) P.M. Buscema, E. Grossi, A. Bronstein, L. Weldon, M. Asadi-Zeydabadi, R. Benzi, F. Newman, A New Algorithm for Identifying Possible Epidemic Sources with Application to the German Escherichia Coli Outbreak, in a Special Issue “Spatial Analysis and Data Mining”, ISPRS International Journal of Geo-Information, 2013, 2(1):155-200.
6) P.M.Buscema, P. L. Sacco, G. Ferilli, M. Breda, E. Grossi, Analyzing the semantics of point spaces through the topological weighted centroid and other mathematical quantities: the hidden geometry of the global economic order, Computational Intelligence, Volume 0, Number 0, 2014, doi: 10.1111/coin.12040.