In this paper, we first proposed the supervised version of probabilistic principal component analysis mixture model. Then, we consider a learning predictive model with projection penalties, as an approach for dimensionality reduction without loss of information for face recognition. In the proposed method, first a local linear underlying manifold of data samples is obtained using the supervised probabilistic principal component analysis mixture model. Then, a support vector machine classifier with projection penalty is trained as a predictive model using this local linear manifold. Thus, the predictive model benefits from dimensionality reduction, while it loses minimum amount of useful information. To evaluate the proposed method, we used well-known face recognition databases. Gabor feature extraction method have been applied to these images. The experimental results show that the proposed method has a higher classification accuracy than many of the traditional methods which use predictive models after dimensionality reduction. It also works better than the projection penalty method with linear or nonlinear based dimensionality reduction models.
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