Clustering in Financial Markets

This chapter considers graph partition of a particular kind of complex networks referred to as power law graphs. In particular, we focus our analysis on the market graph, constructed from time series of price return on the American stock market. Two different methods originating from clustering analysis in social networks and image segmentation are applied to obtain graph partitions and the results are evaluated in terms of the structure and quality of the partition. Our results show that the market graph possesses a clear clustered structure only for higher correlation thresholds. By studying the internal structure of the graph clusters we found that they could serve as an alternative to traditional sector classification of the market. Finally, partitions for different time series were considered to study the dynamics and stability in the partition structure. Even though the results from this part were not conclusive we think this could be an interesting topic for future research.

[1]  Eli Upfal,et al.  Stochastic models for the Web graph , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[2]  Chris Hankin,et al.  Fast Multi-Scale Detection of Relevant Communities in Large-Scale Networks , 2013, Comput. J..

[3]  Panos M. Pardalos,et al.  Mining market data: A network approach , 2006, Comput. Oper. Res..

[4]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[6]  Donald F. Towsley,et al.  On distinguishing between Internet power law topology generators , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[7]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[8]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[9]  Panos M. Pardalos,et al.  Network approach for the Russian stock market , 2014, Comput. Manag. Sci..

[10]  Javier Martín Hernández,et al.  A qualitative comparison of power law generators , 2006 .

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[12]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[13]  Béla Bollobás,et al.  Random Graphs: Notation , 2001 .

[14]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

[15]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[16]  Jon M. Kleinberg,et al.  The Web as a Graph: Measurements, Models, and Methods , 1999, COCOON.

[17]  Ulrik Brandes,et al.  On Modularity Clustering , 2008, IEEE Transactions on Knowledge and Data Engineering.

[18]  Panos M. Pardalos,et al.  Statistical analysis of financial networks , 2005, Comput. Stat. Data Anal..

[19]  Xintian Zhuang,et al.  A network analysis of the Chinese stock market , 2009 .

[20]  B. Bollobás.  The evolution of random graphs , 1984 .

[21]  Hideo Matsuda,et al.  Classifying Molecular Sequences Using a Linkage Graph With Their Pairwise Similarities , 1999, Theor. Comput. Sci..

[22]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[23]  Pan Hui,et al.  Handbook of Optimization in Complex Networks , 2012 .

[24]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[25]  Fan Chung Graham,et al.  A random graph model for massive graphs , 2000, STOC '00.

[26]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[27]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Christos Faloutsos,et al.  Graphs over time: densification laws, shrinking diameters and possible explanations , 2005, KDD '05.

[29]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[30]  Chris Hankin,et al.  Fast Multi-Scale Detection of Relevant Communities , 2012, ArXiv.

[31]  L. Hubert,et al.  Comparing partitions , 1985 .

[32]  Sergiy Butenko,et al.  Clique Relaxation Models in Social Network Analysis , 2012 .