On the Multiplicative Regularization of Graph Laplacians on Closed and Open Structures With Applications to Spectral Partitioning

A new regularization technique for graph Laplacians arising from triangular meshes of closed and open structures is presented. The new technique is based on the analysis of graph Laplacian spectrally equivalent operators in terms of Sobolev norms and on the appropriate selection of operators of opposite differential strength to achieve a multiplicative regularization. In addition, a new 3-D/2-D nested regularization strategy is presented to deal with open geometries. Numerical results show the advantages of the proposed regularization as well as its effectiveness when used in spectral partitioning applications.