Recent Advances of Manifold Regularization

Semi-supervised learning (SSL) that can make use of a small number of labeled data with a large number of unlabeled data to produce significant improvement in learning performance has been received considerable attention. Manifold regularization is one of the most popular works that exploits the geometry of the probability distribution that generates the data and incorporates them as regularization terms. There are many representative works of manifold regularization including Laplacian regularization (LapR), Hessian regularization (HesR) and p-Laplacian regularization (pLapR). Based on the manifold regularization framework, many extensions and applications have been reported. In the chapter, we review the LapR and HesR, and we introduce an approximation algorithm of graph p-Laplacian. We study several extensions of this framework for pairwise constraint, p-Laplacian learning, hypergraph learning, etc

A Third Order based Additional Regularization in Intrinsic Space of the Manifold

Second order graph Laplacian regularization has the limitation that the solution remains biased towards a constant which restricts its extrapolationcapability. The lack of extrapolation results in poor generalization. An additional penalty factor is needed on the function to avoid its over-fitting on seen unlabeled training instances. The third order derivative based technique identifies the sharp variations in the function and accurately penalizes them to avoid overfitting. The resultant function leads to a more accurate and generic model that exploits the twist and curvature variations on the manifold. Extensive experiments on synthetic and real-world data set clearly shows thatthe additional regularization increases accuracy and generic nature of model

Visual Understanding via Multi-Feature Shared Learning with Global Consistency

Image/video data is usually represented with multiple visual features. Fusion of multi-source information for establishing the attributes has been widely recognized. Multi-feature visual recognition has recently received much attention in multimedia applications. This paper studies visual understanding via a newly proposed l_2-norm based multi-feature shared learning framework, which can simultaneously learn a global label matrix and multiple sub-classifiers with the labeled multi-feature data. Additionally, a group graph manifold regularizer composed of the Laplacian and Hessian graph is proposed for better preserving the manifold structure of each feature, such that the label prediction power is much improved through the semi-supervised learning with global label consistency. For convenience, we call the proposed approach Global-Label-Consistent Classifier (GLCC). The merits of the proposed method include: 1) the manifold structure information of each feature is exploited in learning, resulting in a more faithful classification owing to the global label consistency; 2) a group graph manifold regularizer based on the Laplacian and Hessian regularization is constructed; 3) an efficient alternative optimization method is introduced as a fast solver owing to the convex sub-problems. Experiments on several benchmark visual datasets for multimedia understanding, such as the 17-category Oxford Flower dataset, the challenging 101-category Caltech dataset, the YouTube & Consumer Videos dataset and the large-scale NUS-WIDE dataset, demonstrate that the proposed approach compares favorably with the state-of-the-art algorithms. An extensive experiment on the deep convolutional activation features also show the effectiveness of the proposed approach. The code is available on http://www.escience.cn/people/lei/index.htmlComment: 13 pages,6 figures, this paper is accepted for publication in IEEE Transactions on Multimedi