@article{oai:tokyo-metro-u.repo.nii.ac.jp:00007165,
 author = {Hirakura, Naoki and Takano, Chisa and Aida, Masaki},
 journal = {The 2018 International Symposium on Nonlinear Theory and its Applications (NOLTA 2018)},
 month = {},
 note = {It is inherent difficult to directly quantify the structure of the social networks that describe human relations. The network resonance method was proposed to elucidate the unknown Laplacian matrix representing social network structure. This method gives information on the eigenvalues and eigenvectors of the Laplacian matrix from observations of the dynamics of a social network. If all the eigenvalues and eigenvectors are known, the original Laplacian matrix can be determined. One problem with the network resonance method is that only limited information about eigenvectors can be acquired, and only the absolute values of the vector elements are available. Therefore, to determine the Laplacian matrix, it is necessary to determine the signs of each element of the eigenvectors; this task has order of O(2^n) given the combinations of n users for every eigenvector. This paper proposes a method that determines eigenvector element signs efficiently by running a sign determination algorithm in parallel and uses only those with fewer calculation amount. The proposal executes sign determination in polynomial time. We also reduce the calculation overhead by applying compressed sensing; the computational complexity of sign determination is reduced to almost O(n^2)., postprint},
 pages = {180--183},
 title = {Efficient Orthogonalizing the Eigenvectors of the Laplacian Matrix to Estimate Social Network Structure},
 volume = {2018},
 year = {2018}
}