Diffuse Interface Models on Graphs for Classification of High Dimensional Data
CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS
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There are currently several communities working on algorithms for classi cation of high dimensional data. This work develops a class of variational algorithms that combine recent ideas from spectral methods on graphs with nonlinear edgeregion detection methods traditionally used in in the PDE-based imaging community. The algorithms are based on the Ginzburg-Landau functional which has classical PDE connections to total variation minimization. Convex-splitting algorithms allow us to quickly nd minimizers of the proposed model and take advantage of fast spectral solvers of linear graph-theoretic problems. We present diverse computational examples involving both basic clustering and semi-supervised learning for di erent applications. Case studies include feature identi cation in images, segmentation in social networks, and segmentation of shapes in high dimensional datasets.
- Theoretical Mathematics