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Diffuse Interface Models on Graphs for Classification of High Dimensional Data
- Source :
- SIAM Review, vol 58, iss 2, Bertozzi, AL; & Flenner, A. (2016). Diffuse Interface Models on Graphs for Classification of High Dimensional Data. SIAM Review, 58(2), 293-328. doi: 10.1137/16M1070426. UCLA: Retrieved from: http://www.escholarship.org/uc/item/4hs5472g, SIAM REVIEW, vol 58, iss 2
- Publication Year :
- 2016
- Publisher :
- eScholarship, University of California, 2016.
-
Abstract
- This paper is a republication of an MMS paper [A. L. Bertozzi and A. Flenner, Multiscale Model. Simul., 10 (2012), pp. 1090--1118] describing a new class of algorithms for classification of high dimensional data. These methods combine ideas from spectral methods on graphs with nonlinear edge/region detection methods traditionally used in the PDE-based imaging community. The algorithms use the Ginzburg--Landau functional, extended to a graphical framework, which has classical PDE connections to total variation minimization. Convex splitting algorithms allow us to quickly find minimizers of the proposed model and take advantage of fast spectral solvers of linear graph-theoretic problems. We review the diverse computational examples presented in the original paper, involving both basic clustering and semisupervised learning for different applications. Case studies include feature identification in images, segmentation in social networks, and segmentation of shapes in high dimensional datasets. Since the pape...
- Subjects :
- Clustering high-dimensional data
Theoretical computer science
Interface (Java)
Computation
high dimensional data
General Physics and Astronomy
Numerical & Computational Mathematics
Image processing
02 engineering and technology
01 natural sciences
Theoretical Computer Science
0202 electrical engineering, electronic engineering, information engineering
Feature (machine learning)
Segmentation
0101 mathematics
Electrical and Electronic Engineering
Cluster analysis
Mathematics
Ecological Modeling
Applied Mathematics
Nystrom extension
General Chemistry
diffuse interfaces
Computer Science Applications
image processing
010101 applied mathematics
Computational Mathematics
Nonlinear system
Networking and Information Technology R&D
Modeling and Simulation
020201 artificial intelligence & image processing
Spectral method
Algorithm
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- SIAM Review, vol 58, iss 2, Bertozzi, AL; & Flenner, A. (2016). Diffuse Interface Models on Graphs for Classification of High Dimensional Data. SIAM Review, 58(2), 293-328. doi: 10.1137/16M1070426. UCLA: Retrieved from: http://www.escholarship.org/uc/item/4hs5472g, SIAM REVIEW, vol 58, iss 2
- Accession number :
- edsair.doi.dedup.....c23845894684861f894924d737d6fa10