A tool for filtering information in complex systems.

By Michele Tumminello, Tomaso Aste, T. Di Matteo, Rosario Nunzio Mantegna. Proceedings of the National Academy of Sciences of the United States of America, 2005

879 citations recorded by the source corpus.

We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c936251bf543ac483b18d694f9c05a8a7ada15c5

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Citations in the corpus

Multiscale Embedded Gene Co-expression Network Analysis (2015, methodology): “PCP is a key technique developed to speed up PFN construction to overcome the worst case O(|V|(3)) complexity of the existing serial PMFG algorithm (SeeMethods for detailed discussion) [21, 27].”
Investigating the structure of semantic networks in low and high creative persons (2014, methodology): “To overcome this obstacle, we make use of the Planar Maximally Filtered Graph (PMFG; Tumminello et al., 2005) to construct from the complete network a sub-graph that captures the most relevant information embedded in the original network.”
Disrupted Modularity and Local Connectivity of Brain Functional Networks in Childhood-Onset Schizophrenia (2010, neutral): “…in Systems Neuroscience www.frontiersin.org October 2010 | Volume 4 | Article 147 | 13 global threshold to a correlation matrix have previously been documented in physics and economics, and several alternatives have been proposed (Onnela et al., 2002; Tumminello et al., 2005; Serrano et al., 2009).”
Extreme risk spillover network: application to financial institutions (2017, methodology): “The dynamic ND and GE of time-varying 1% VaR networks increase as the lag order †In previous research, Wang et al. (2010) and Liu and Wan (2011), who, respectively, investigate cross-correlations between the Chinese A-Share and B-Share markets and between crude oil spot and futures markets using rol”
The statistical physics of real-world networks (2018, background): “The problem of building a statistically validated projection of a bipartite network is similar in spirit to that of extracting the backbone from standard weighted networks [80–83], and has been typically addressed by determining which links are significant using a threshold— either unconditional or ”
Correlation, Hierarchies, and Networks in Financial Markets (2008, neutral): “Useful examples of correlation based networks different from the minimum spanning tree are the planar maximally filtered graph (Tumminello et al., 2005) and the average linkage minimum spanning tree (Tumminello et al., 2007c).”
Investigating the performance of Exploratory Graph analysis and traditional techniques to identify the number of latent factors: a simulation and tutorial (2018, background): “A planar network is a network that could be drawn on a sphere with no edges crossing (Figure 3; often, however, the networks are depicted with edges crossing; Tumminello, Aste, Di Matteo, & Mantegna, 2005).”
Correlation structure and dynamics in volatile markets (2010, methodology): “) The algorithm to build such a graph is identical to the one for the MST discussed previously, except that at step 3 the condition to accept the link now requires that the resulting graph must be embeddable on a surface of genus g [19, 20, 24].”
A new approach to quantify power-law cross-correlation and its application to commodity markets (2011, background): “Many simultaneously recorded time series in various real world commodity or financial markets are found to exhibit spatial or temporal cross-correlations [3, 7-17].”
A network perspective of the stock market (2010, methodology): “In order to retain more information about the networks, less drastic filtering may be applied, e.g., using Planar Maximally Filtered Graph (PMFG), as proposed by Tumminello et al. (2005).”
Correlation structure and dynamics of international real estate securities markets: A network perspective (2015, methodology): “[33] design the PMFG method, which retains the powerful filtering features of the MST approach and includes additional links, cycles, and cliques.”