Math @ Duke

Publications [#343643] of Robert Calderbank
Papers Published
 Zhu, W; Qiu, Q; Huang, J; Calderbank, R; Sapiro, G; Daubechies, I, LDMNet: Low Dimensional Manifold Regularized Neural Networks,
Proceedings of the Ieee Computer Society Conference on Computer Vision and Pattern Recognition
(December, 2018),
pp. 27432751 [doi]
(last updated on 2019/10/16)
Abstract: © 2018 IEEE. Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are dataindependent. Datadependent regularizations are mostly motivated by the observation that data of interest lie close to a manifold, which is typically hard to parametrize explicitly. These methods usually only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose the LowDimensionalManifoldregularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low dimensional manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the manifold dimension as a regularization term in a variational functional. The resulting EulerLagrange equation is a LaplaceBeltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. In the experiments, we show that LDMNet significantly outperforms widelyused regularizers. Moreover, LDMNet can extract common features of an object imaged via different modalities, which is very useful in realworld applications such as crossspectral face recognition.


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