Out-of-sample generalizations for supervised manifold learning for classification

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets

Subspace-Based Holistic Registration for Low-Resolution Facial Images

Subspace-based holistic registration is introduced as an alternative to landmark-based face registration, which has a poor performance on low-resolution images, as obtained in camera surveillance applications. The proposed registration method finds the alignment by maximizing the similarity score between a probe and a gallery image. We use a novel probabilistic framework for both user-independent as well as user-specific face registration. The similarity is calculated using the probability that the face image is correctly aligned in a face subspace, but additionally we take the probability into account that the face is misaligned based on the residual error in the dimensions perpendicular to the face subspace. We perform extensive experiments on the FRGCv2 database to evaluate the impact that the face registration methods have on face recognition. Subspace-based holistic registration on low-resolution images can improve face recognition in comparison with landmark-based registration on high-resolution images. The performance of the tested face recognition methods after subspace-based holistic registration on a low-resolution version of the FRGC database is similar to that after manual registration