Archetypal networks

In this paper we propose a method to analyze and synthesize a set of N networks that refer to a common scenario and that are comparable among each other. Examples of this type of data are: a set of collaboration networks, each defined for a different scientific field; or a set of ego networks, where egos belong to a same category; a set of governance networks, etc. For these kind of sets of networks it can be of interest to find a small number of representative networks that can serve as a condensed view of the data set. In a statistical perspective this goal amount to find a small number of networks that are able to typify the network structures starting from the observed ones. In addition, these networks should have a clear and interpretable profile in terms of their most relevant features and their specificity in contrast to the others. Given the set of N networks, we propose to find these representative networks by using the archetypal analysis, yielding what we call Archetypal Networks. The Archetypal Networks can serve to understand the data structure, as benchmarks for the other networks, and are useful also to compare networks among each other. We exemplify the proposed procedure by analyzing a set of 36 governance networks of public structures devoted to provide youth services and referring to 36 different territorial districts in Campania region in Italy. Our results highlight the presence of different network structures that can be interpreted in terms of the governance forms established in literature.

[1]  K. Kersting,et al.  Early drought stress detection in cereals: simplex volume maximisation for hyperspectral image analysis. , 2012, Functional plant biology : FPB.

[2]  S M Shortell,et al.  A taxonomy of health networks and systems: bringing order out of chaos. , 1999, Health services research.

[3]  Emily Stone.  Exploring archetypal dynamics of pattern formation in cellular flames , 2002 .

[4]  Leigh Morris,et al.  Consumer Archetypes: A New Approach to Developing Consumer Understanding Frameworks , 2006, Journal of Advertising Research.

[5]  S. Marinetti,et al.  Archetypes and principal components of an IR image sequence , 2007 .

[6]  Giancarlo Ragozini,et al.  On the use of archetypes as benchmarks , 2008 .

[7]  Luka Kronegger,et al.  Collaboration structures in Slovenian scientific communities , 2012, Scientometrics.

[8]  Jukka-Pekka Onnela,et al.  Taxonomies of networks from community structure. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Giancarlo Ragozini,et al.  ARCHETYPAL ANALYSIS FOR INTERVAL DATA IN MARKETING RESEARCH 1 , 2006 .

[10]  Giancarlo Ragozini,et al.  Interval Archetypes: A New Tool for Interval Data Analysis , 2012, Stat. Anal. Data Min..

[11]  Hamideh Afsarmanesh,et al.  Taxonomy of collaborative networks forms: FInES Task Force on Collaborative Networks and SOCOLNET - Society of Collaborative Networks , 2012 .

[12]  Richard T. Carson,et al.  Archetypal analysis: a new way to segment markets based on extreme individuals , 2003 .

[13]  E. Wegman.  Hyperdimensional Data Analysis Using Parallel Coordinates , 1990 .

[14]  Alfred Inselberg,et al.  The plane with parallel coordinates , 1985, The Visual Computer.

[15]  Adele Cutler,et al.  Introduction to archetypal analysis of spatio-temporal dynamics , 1996 .

[16]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[17]  L. Finesso,et al.  Matrix factorization methods: Application to thermal NDT/E , 2006 .

[18]  Cristina Chaminade.  Global Innovation Networks: Towards a Taxonomy , 2012 .

[19]  Morten Mørup,et al.  Archetypal analysis of diverse Pseudomonas aeruginosa transcriptomes reveals adaptation in cystic fibrosis airways , 2013, BMC Bioinformatics.

[20]  Rajkumar Buyya,et al.  A Taxonomy and Survey of Content Delivery Networks , 2006 .

[21]  R. Lamming,et al.  A Taxonomy of Supply Networks , 2001 .

[22]  Christian Bauckhage,et al.  A Note on Archetypal Analysis and the Approximation of Convex Hulls , 2014, ArXiv.

[23]  Volker Roth,et al.  Automatic Model Selection in Archetype Analysis , 2012, DAGM/OAGM Symposium.

[24]  Ulrik Brandes,et al.  Longitudinal analysis of personal networks. The case of Argentinean migrants in Spain , 2010, Soc. Networks.

[25]  B. Chan,et al.  Archetypal analysis of galaxy spectra , 2003, astro-ph/0301491.

[26]  P. Lockhart,et al.  Introduction to Geometry , 1940, The Mathematical Gazette.

[27]  Christian Seiler,et al.  Archetypal Scientists , 2012, J. Informetrics.

[28]  C. Ji.  An Archetypal Analysis on , 2005 .

[29]  Giancarlo Ragozini,et al.  Exploring Data Through Archetypes , 2010 .

[30]  Lior Pachter,et al.  Toward the Human Genotope , 2007, Bulletin of mathematical biology.

[31]  Manuel J. A. Eugster,et al.  Performance Profiles based on Archetypal Athletes , 2012 .