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Network Distances for Weighted Digraphs

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Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1275))

Abstract

The interpretation of the biological mechanisms through the systems biology approach involves the representation of the molecular components in an integrated system, namely a network, where the interactions among them are much more informative than the single components. The definition of the dissimilarity between complex biological networks is fundamental to understand differences between conditions, states, and treatments. It is, therefore, challenging to identify the most suitable distance measures for this kind of analysis. In this work, we aim at testing several measures to define the distance among sample- and condition-specific metabolic networks. The networks are represented as directed, weighted graphs, due to the nature of the metabolic reactions. We used four different case studies and exploited Support Vector Machine classification to define the performance of each measure.

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Acknowledgments

The work was carried out also within the activities of the authors as members of the INdAM Research group GNCS.

Author information

Authors and Affiliations

  1. Institute for High-Performance Computing and Networking, National Research Council, Naples, Italy

    Ilaria Granata, Mario Rosario Guarracino, Lucia Maddalena & Ichcha Manipur

  2. University of Cassino and Southern Lazio, Cassino, Italy

    Mario Rosario Guarracino

Authors
  1. Ilaria Granata
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  2. Mario Rosario Guarracino
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  3. Lucia Maddalena
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  4. Ichcha Manipur
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Corresponding author

Correspondence to Mario Rosario Guarracino .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  3. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia

    Tatiana Gruzdeva

Appendix

Appendix

In Tables 9 and 10, we report detailed numerical performance results obtained using the considered network distances over Simplifications 1 and 2 of all datasets, plotted in Figs. 3(a) and (b), respectively. To provide deeper insight into the performance with respect to each class c, besides Accuracy (Acc) as defined in Eq. (9), we further consider Sensitivity (Se) and Specificity (Sp), defined as

$$ Se = \frac{TP_c}{TP_c + FN_c},\; \; \; \; Sp = \frac{TN_c}{TN_c + FP_c}. $$

Here, \(TP_c\) and \(FN_c\) indicate the number of samples belonging to class c that are correctly classified in class c and those that are misclassified, respectively; \(TN_c\) and \(FP_c\) indicate the number of samples that do not belong to class c that are correctly classified as not belonging to it and those that are misclassified as belonging to it, respectively. Having considered binary classification problems, Se for Class 1 coincides with Sp for Class 2; likewise, Sp for Class 1 coincides with Se for Class 2.

Table 9. Average accuracy (Acc), Sensitivity (Se) and Specificity (Sp) for Class 1 of all datasets (Simplification 1). Highest Acc for each dataset in bold.
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Table 10. Average accuracy (Acc), Sensitivity (Se) and Specificity (Sp) for Class 1 of all datasets (Simplification 2). Highest Acc for each dataset in bold.
Full size table

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Granata, I., Guarracino, M.R., Maddalena, L., Manipur, I. (2020). Network Distances for Weighted Digraphs. In: Kochetov, Y., Bykadorov, I., Gruzdeva, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Communications in Computer and Information Science, vol 1275. Springer, Cham. https://doi.org/10.1007/978-3-030-58657-7_31

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  • DOI: https://doi.org/10.1007/978-3-030-58657-7_31

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