The rapid development of computer hardware and Internet technology makes large scale data dependent models computationally tractable, and opens a bright avenue for annotating images through innovative machine learning algorithms. Semisupervised learning (SSL) therefore received intensive attention in recent years and was successfully deployed in image annotation. One representative work in SSL is Laplacian regularization (LR), which smoothes the conditional distribution for classification along the manifold encoded in the graph Laplacian, however, it is observed that LR biases the classification function toward a constant function that possibly results in poor generalization. In addition, LR is developed to handle uniformly distributed data (or single-view data), although instances or objects, such as images and videos, are usually represented by multiview features, such as color, shape, and texture. In this paper, we present multiview Hessian regularization (mHR) to address the above two problems in LR-based image annotation. In particular, mHR optimally combines multiple HR, each of which is obtained from a particular view of instances, and steers the classification function that varies linearly along the data manifold. We apply mHR to kernel least squares and support vector machines as two examples for image annotation. Extensive experiments on the PASCAL VOC'07 dataset validate the effectiveness of mHR by comparing it with baseline algorithms, including LR and HR.

In recent years, the advances in data collection and statistical analysis promotes canonical correlation analysis (CCA) available for more advanced research. CCA is the main technique for two-set data dimensionality reduction such that the correlation between the pairwise variables in the common subspace is mutually maximized. Over 80-years of developments, a number of CCA models have been proposed according to different machine learning mechanisms. However, the field lacks an insightful review for the state-of-art developments. This survey targets to provide a well-organized overview for CCA and its extensions. We first review the CCA theory from the perspective of both model formation and model optimization. Following that, we present a taxonomy of current progress and classify them into seven groups: 1) multi-view CCA, 2) probabilistic CCA, 3) deep CCA, 4) kernel CCA, 5) discriminative CCA, 6) sparse CCA and 7) locality preserving CCA. For each group, we demonstrate two or three representative mathematical models, identifying their strengths and limitations. We summarize the representative applications and numerical results of these seven groups in real-world practices, collecting the data sets and open-sources for implementation. In the end, we provide several promising future research directions that can improve the current state of the art.

The explosive growth of multimedia data on the Internet makes it essential to develop innovative machine learning algorithms for practical applications especially where only a small number of labeled samples are available. Manifold regularized semi-supervised learning (MRSSL) thus received intensive attention recently because it successfully exploits the local structure of data distribution including both labeled and unlabeled samples to leverage the generalization ability of a learning model. Although there are many representative works in MRSSL, including Laplacian regularization (LapR) and Hessian regularization, how to explore and exploit the local geometry of data manifold is still a challenging problem. In this paper, we introduce a fully efficient approximation algorithm of graph p-Laplacian, which significantly saving the computing cost. And then we propose p-LapR (pLapR) to preserve the local geometry. Specifically, p-Laplacian is a natural generalization of the standard graph Laplacian and provides convincing theoretical evidence to better preserve the local structure. We apply pLapR to support vector machines and kernel least squares and conduct the implementations for scene recognition. Extensive experiments on the Scene 67 dataset, Scene 15 dataset, and UC-Merced dataset validate the effectiveness of pLapR in comparison to the conventional manifold regularization methods.

Graph-based and manifold-regularization (MR)-based semisupervised learning, including Laplacian regularization (LapR) and hypergraph LapR (HLapR), have achieved prominent performance in preserving locality and similarity information. However, it is still a great challenge to exactly explore and exploit the local structure of the data distribution. In this paper, we present an efficient and effective approximation algorithm of hypergraph ${p}$ -Laplacian and then propose hypergraph ${p}$ -LapR (HpLapR) to preserve the geometry of the probability distribution. In particular, hypergraph is a generalization of a standard graph while hypergraph ${p}$ -Laplacian is a nonlinear generalization of the standard graph Laplacian. The proposed HpLapR shows great potential to exploit the local structures. We integrate HpLapR with logistic regression for remote sensing image recognition. Experiments on UC-Merced data set demonstrate that the proposed HpLapR has superior performance compared with several popular MR methods including LapR and HLapR.