Network Decomposition and Complexity Measures: An Information Geometrical Approach
We consider the graph representation of the stochastic model with n binary variables, and develop an information theoretical framework to measure the degree of statistical association existing between subsystems as well as the ones represented by each edge of the graph representation. Besides, we co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/7/4132 |
| _version_ | 1798042034336956416 |
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| author | Masatoshi Funabashi |
| author_facet | Masatoshi Funabashi |
| author_sort | Masatoshi Funabashi |
| collection | DOAJ |
| description | We consider the graph representation of the stochastic model with n binary variables, and develop an information theoretical framework to measure the degree of statistical association existing between subsystems as well as the ones represented by each edge of the graph representation. Besides, we consider the novel measures of complexity with respect to the system decompositionability, by introducing the geometric product of Kullback–Leibler (KL-) divergence. The novel complexity measures satisfy the boundary condition of vanishing at the limit of completely random and ordered state, and also with the existence of independent subsystem of any size. Such complexity measures based on the geometric means are relevant to the heterogeneity of dependencies between subsystems, and the amount of information propagation shared entirely in the system. |
| first_indexed | 2024-04-11T22:29:51Z |
| format | Article |
| id | doaj.art-0be0518c671f4aeaa5e54d93ec721979 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:29:51Z |
| publishDate | 2014-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0be0518c671f4aeaa5e54d93ec7219792022-12-22T03:59:29ZengMDPI AGEntropy1099-43002014-07-011674132416710.3390/e16074132e16074132Network Decomposition and Complexity Measures: An Information Geometrical ApproachMasatoshi Funabashi0Sony Computer Science Laboratories, inc. Takanawa muse bldg. 3F, 3-14-13, Higashi Gotanda, Shinagawa-ku, Tokyo 141-0022, JapanWe consider the graph representation of the stochastic model with n binary variables, and develop an information theoretical framework to measure the degree of statistical association existing between subsystems as well as the ones represented by each edge of the graph representation. Besides, we consider the novel measures of complexity with respect to the system decompositionability, by introducing the geometric product of Kullback–Leibler (KL-) divergence. The novel complexity measures satisfy the boundary condition of vanishing at the limit of completely random and ordered state, and also with the existence of independent subsystem of any size. Such complexity measures based on the geometric means are relevant to the heterogeneity of dependencies between subsystems, and the amount of information propagation shared entirely in the system.http://www.mdpi.com/1099-4300/16/7/4132information geometrycomplexity measurecomplex networksystem decompositionabilitygeometric mean |
| spellingShingle | Masatoshi Funabashi Network Decomposition and Complexity Measures: An Information Geometrical Approach Entropy information geometry complexity measure complex network system decompositionability geometric mean |
| title | Network Decomposition and Complexity Measures: An Information Geometrical Approach |
| title_full | Network Decomposition and Complexity Measures: An Information Geometrical Approach |
| title_fullStr | Network Decomposition and Complexity Measures: An Information Geometrical Approach |
| title_full_unstemmed | Network Decomposition and Complexity Measures: An Information Geometrical Approach |
| title_short | Network Decomposition and Complexity Measures: An Information Geometrical Approach |
| title_sort | network decomposition and complexity measures an information geometrical approach |
| topic | information geometry complexity measure complex network system decompositionability geometric mean |
| url | http://www.mdpi.com/1099-4300/16/7/4132 |
| work_keys_str_mv | AT masatoshifunabashi networkdecompositionandcomplexitymeasuresaninformationgeometricalapproach |