TY - JOUR
T1 - The 1-Laplacian Cheeger Cut: Theory and Algorithms
AU - Chang , K.C.
AU - Shao , Sihong
AU - Zhang , Dong
JO - Journal of Computational Mathematics
VL - 5
SP - 443
EP - 467
PY - 2015
DA - 2015/10
SN - 33
DO - http://doi.org/10.4208/jcm.1506-m2014-0164
UR - https://global-sci.org/intro/article_detail/jcm/9854.html
KW - Spectral graph theory, Spectral clustering, 1-Laplace operator, Graph Laplacian, Eigenvalue problems, Cheeger constant, Graph cut, Optimization, Convergence
AB - <p style="text-align: justify;">This paper presents a detailed review of both theory and algorithms for the Cheeger cut based on the graph 1-Laplacian. In virtue of the cell structure of the feasible set, we propose a cell descend (CD) framework for achieving the Cheeger cut. While plugging the relaxation to guarantee the decrease of the objective value in the feasible set, from which both the inverse power (IP) method and the steepest descent (SD) method can also be recovered, we are able to get two specified CD methods. Comparisons of all these methods are conducted on several typical graphs.</p>