This paper proposes a semi-supervised inductive algorithm adopting a Gaussian random field (GRF) and Gaussian process. We introduce the prior based on graph regularization. This regularization term measures the p-smoothness over the graph. A new conditional probability called the extended Bernoulli model (EBM) is also proposed. EBM generalizes the logistic regression to the semi-supervised case, and especially, it can naturally represent the margin. In the training phase, a novel solution is given to the discrete regularization framework defined on the graphs. For the new test data, we present the prediction formulation, and explain how the margin model affects the classification boundary. A hyper-parameter estimation method is also developed. Experimental results show that our method is competitive with the existing semi-supervised inductive and transductive methods.
SONG Yangqiu, LEE Jianguo, ZHANG Changshui, XIANG Shiming
. Semi-supervised Gaussian random field transduction
and induction[J]. Frontiers of Electrical and Electronic Engineering, 2008
, 3(1)
: 1
-9
.
DOI: 10.1007/s11460-008-0001-y
1. Zhu X Semi-supervisedlearning literature surveyTechnical Report,Computer SciencesUniversity of Wisconsin-Madison 2005
2. Belkin M Niyogi P Sindhwani. Manifold regularization: a geometric framework for learningfrom labeled and unlabeled examplesJournalof Machine Learning Research 2006 723992434
3. Zhou D Bousquet O Lal T N et al.Learning with local and global consistencyProceedings of Advances in Neural Information ProcessingSystems 2004 16321328
4. Zhou D Schölkopf B Regularization on discretespacesProceedings of the 27th DAGM Symposium 2005 361368
5. Zhu X Ghahramani Z Lafferty J Semi-supervised learning using Gaussian fields and harmonicfunctionsProceedings of the 20th InternationalConference of Machine Learning 2003 912919
6. Williams C Barber D Bayesian classification withGaussian processesIEEE Transactions onPattern Analysis and Machine Intelligence 1998 20(12)13421351
7. Chung F SpectralGraph Theory. No. 92 in Tegional Conference Series in Mathematics. American Mathematical Society1997
8. Lawrence N D Jordan M I Semi-supervised learning viaGaussian processesProceedings of Advancesin Neural Information Processing Systems 2004 17753760
9. Neal R M Monte-carloimplementation of Gaussian process models for Bayesian regressionand classificationTechnical Report, Departmentof Statistics, University of Toronto 1997
10. Zhu X Ghahramani Z Semi-supervised learning: fromGaussian fields to Gaussian processesTechnicalReport, Carnegie Mellon University 2003
11. Chang C Lin C Libsvm: A Library for SupportVector Machines 2001