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Full-Text Articles in Physical Sciences and Mathematics
An Adaptive Total Variation Algorithm For Computing The Balanced Cut Of A Graph, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht
An Adaptive Total Variation Algorithm For Computing The Balanced Cut Of A Graph, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht
Mathematics Faculty Works
We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced cut energy as well as convergence of the algorithm. In practice the total variation minimization step is never solved exactly. Instead, an accuracy parameter is specified and the total variation minimization terminates once this level of accuracy is reached. The choice of this parameter can vastly impact both the computational time of the overall algorithm as well as the accuracy of …
Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht
Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht
Mathematics Faculty Works
Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.