Differential geometric regularization for supervised learning of classifiers
Files
Published version
Date
2016
DOI
Authors
Bai, Qinxun
Rosenberg, Steven
Wu, Zheng
Sclaroff, Stan
Version
Published version
OA Version
Citation
Q Bai, S Rosenberg, Z Wu, S Sclaroff. 2016. "Differential geometric regularization for supervised learning of classifiers." Proc. International Conf. on Machine Learning (ICML).
Abstract
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 an estimator of the class probability P(y|\vec 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. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.