Publication

Compact form of the pseudo-inverse matrix in the approximation of a star graph using the conductance electrical model (CEM)

Conference Article

Conference

Joint IAPR International Workshop on Structural, Syntactic and Statistical Pattern Recognition (SSPR&SPR)

Edition

14th

Pages

539-547

Doc link

http://dx.doi.org/10.1007/978-3-642-34166-3_59

File

Download the digital copy of the doc pdf document

Abstract

The Conductance Electrical Model (CEM) translate a graph into a circuit. After applying the model, in many cases, it is necessary to approximate the circuit obtained by a star circuit and this requires the calculation of the Moore–Penrose pseudoinverse of a matrix for which there is a general formula that requires transpose, multiply and invert matrices. But in this particular case, the matrix has a peculiar structure, exploited this peculiar structure in this paper show that the pseudoinverse can be obtained without recourse to the general formula. We demonstrate a closed formula that gives the values of the elements of the pseudoinverse directly without iteration, no longer necessary to multiply or inverter matrices. This improved method eliminates the problems due to computer rounding and due to bad-conditioned problems in mathematical terms.



Categories

pattern recognition.

Author keywords

inexact isomorphism graph matching, conductance electrical model, graph matching

Scientific reference

M. Igelmo and A. Sanfeliu. Compact form of the pseudo-inverse matrix in the approximation of a star graph using the conductance electrical model (CEM), 14th Joint IAPR International Workshop on Structural, Syntactic and Statistical Pattern Recognition, 2012, Hiroshima, Japan, in Structural, Syntactic, and Statistical Pattern Recognition, Vol 7626 of Lecture Notes in Computer Science, pp. 539-547, 2012, Springer.