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Multiclass Semi-supervised Learning on Graphs Using Ginzburg-Landau Functional Minimization

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Pattern Recognition Applications and Methods

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 318))

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Abstract

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.

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Acknowledgments

This research has been supported by the Air Force Office of Scientific Research MURI grant FA9550-10-1-0569 and by ONR grant N0001411AF00002.

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Correspondence to Cristina Garcia-Cardona .

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Garcia-Cardona, C., Flenner, A., Percus, A.G. (2015). Multiclass Semi-supervised Learning on Graphs Using Ginzburg-Landau Functional Minimization. In: Fred, A., De Marsico, M. (eds) Pattern Recognition Applications and Methods. Advances in Intelligent Systems and Computing, vol 318. Springer, Cham. https://doi.org/10.1007/978-3-319-12610-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-12610-4_8

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