A Semi-supervied Classification Method Based On Posterior Probability And Manifold Regularization

The semi-supervised classification algorithm framework (Manifold Regularization，MR) and the posterior probability-based support vector machine (Posterior ProbabilitySupport Vector Machine，PPSVM) are both new theories put forward in recent years.However, we found this two methods still have some defects.To solve these problems, we introduce posterior probability knowledge to MRframework, and propose a new semi-supervied classification algorithm framework basedon posterior probability and manifold regularization called PPMR. PPMR takes themanifold regularization technology to find a optimized classification function in thereproducing kernel Hilbert space. This encourages the labeled samples to have similarclassification function values with the labeled values and the neighbour samples includinglabeled samples and unlabeled samples to have similar classification function valuesamong each other. The basic idea is to treat each labeled sample seperately, use posteriorprobability knowledge to indicate the position of labeled samples, and spread the posteriorprobability knowledge by unlabeled samples. This corrects the classification bias causedby the labeled samples located in fuzzy areas, and also take use of unlabeled samples.On the basis of MR, using the posterior probability to label samples directly, weacquire the basic form of PPMR. Improving the regularization coefficient by theexperience scale, we aquire the improved form of PPMR. On this base, we introduce theposterior probability mapping function to convert the posterior probability, and finallyacquire the extended form of PPMR. When we define the abstract loss function as squaredloss and hige loss respecively, we acquire two basic algorithms based on PPMR.In order to further illustrate the PPMR framework and verify the effectiveness ofPPMR, we take a number of repeated random experiments on artificially synthesizeddatasets, public standard datasets and medical application datasets. We discusse severalfactors for PPMR classification results such as kernel function and posterior probabilitymapping function, and compares PPMR with MR and PPSVM on classificationperformance. The results show that the PPMR framework is better in general at accuracyand stability. Especially when some labeled samples lie in the fuzzy boundary area,PPMR generally have greater advantages.