Leave-one-out manifold regularization

Authors:
Jin Yuan;Xuemei Liu;Cheng-Liang Liu
Affiliations:
School of Mechanical and Electronic Engineering, Shandong Agriculture University, Tai'an 271018, China and School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shan ...;School of Mechanical and Electronic Engineering, Shandong Agriculture University, Tai'an 271018, China;School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
Venue:
Expert Systems with Applications: An International Journal
Year:
2012

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Abstract

The manifold regularization (MR) based semi-supervised learning could explore structural relationships from both labeled and unlabeled data. However, the model selection of MR seriously affects its predictive performance due to the inherent additional geometry regularizer of labeled and unlabeled data. In this paper, two continuous and two inherent discrete hyperparameters are selected as optimization variables, and a leave-one-out cross-validation (LOOCV) based Predicted REsidual Sum of Squares (PRESS) criterion is first presented for model selection of MR to choose appropriate regularization coefficients and kernel parameters. Considering the inherent discontinuity of the two hyperparameters, the minimization process is implemented by using a improved Nelder-Mead simplex algorithm to solve the inherent discrete and continues hybrid variables set. The manifold regularization and model selection algorithm are applied to six synthetic and real-life benchmark dataset. The proposed approach, leveraged by effectively exploiting the embedded intrinsic geometric manifolds and unbiased LOOCV estimation, outperforms the original MR and supervised learning approaches in the empirical study.