Abstract:
We deal with the clustering problem in a metric graph. We look for two clusters, and to this end, we study the first nonzero eigenvalue of the p Laplacian on a quantum graph with Newmann or Kirchoff boundary conditions on the nodes. Then, an associated eigenfunction up provides two sets inside the graph, {up > 0} and {up < 0}, which define the clusters. Moreover, we describe in detail the limit cases p→∞and p→1+. © 2016 Project Euclid.
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Citas:
---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D.
(2016)
. Clustering for metric graphs using the p-Laplacian. Michigan Mathematical Journal, 65(3), 451-472.
http://dx.doi.org/10.1307/mmj/1472066142---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D.
"Clustering for metric graphs using the p-Laplacian"
. Michigan Mathematical Journal 65, no. 3
(2016) : 451-472.
http://dx.doi.org/10.1307/mmj/1472066142---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D.
"Clustering for metric graphs using the p-Laplacian"
. Michigan Mathematical Journal, vol. 65, no. 3, 2016, pp. 451-472.
http://dx.doi.org/10.1307/mmj/1472066142---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. Clustering for metric graphs using the p-Laplacian. Mich. Math. J. 2016;65(3):451-472.
http://dx.doi.org/10.1307/mmj/1472066142