A Third Order based Additional Regularization in Intrinsic Space of the Manifold

Rakesh Kumar Yadav, Abhishek Singh, Shekhar Verma, S. Venkatesan, M. Syafrullah, Krisna Adiyarta


Second order graph Laplacian regularization has the limitation that the solution remains biased towards a constant which restricts its extrapolation
capability. The lack of extrapolation results in poor generalization. An additional penalty factor is needed on the function to avoid its over-fitting on seen unlabeled training instances. The third order derivative based technique identifies the sharp variations in the function and accurately penalizes them to avoid overfitting. The resultant function leads to a more accurate and generic model that exploits the twist and curvature variations on the manifold. Extensive experiments on synthetic and real-world data set clearly shows that
the additional regularization increases accuracy and generic nature of model.


Graph Laplacian; Third order derivative; Regularization; Curvature; Manifold

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