Learning with Differential Geometric Regularization


We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust estimator of the class probability P(y|x). The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated.

Paper

[paper] [supplementary] [poster]

Qinxun Bai, Steven Rosenberg, Zheng Wu, and Stan Sclaroff. "Differential Geometric Regularization for Supervised Learning of Classifiers." International Conference on Machine Learning (ICML), 2016.

 

[BibTex]

@inproceedings{Bai2016Georeg,
    title={Differential Geometric Regularization for Supervised Learning of Classifiers},
    author={Bai, Qinxun and Rosenberg, Steve and Wu, Zheng and Sclaroff, Stan},
    booktitle={International Conference on Machine Learning (ICML)},
    year={2016},
  }

Downloads

[code] [data]

We provide a Matlab + C mex implementation of our differential geometric regularization approach, based on an RBF-based representation of the classification function.

Slides