The paper considers the problem of semi-supervised multiview classification, where each view corresponds to a Reproducing Kernel Hilbert Space. An algorithm based on co-regularization methods with extra penalty terms reflecting smoothness and general agreement properties is proposed. We first provide explicit tight control on the Rademacher (L1) complexity of the corresponding class of learners...

Spectral clustering consists of two distinct stages: (a) construct an affinity graph from the dataset and (b) cluster the data points through finding an optimal partition of the affinity graph. The focus of the paper is the first step. Existing spectral clustering algorithms adopt Gaussian function to define the affinity graph since it is easy to implement. However, Gaussian function is hard to...

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original prob...

Multi-label learning refers to the problems where an instance can be assigned to more than one category. In this paper, we present a novel Semi-supervised algorithm for Multi-label learning by solving a Sylvester Equation (SMSE). Two graphs are first constructed on instance level and category level respectively. For instance level, a graph is defined based on both labeled and unlabeled instance...

Resting state activity is brain activation that arises in the absence of any task, and is usually measured in awake subjects during prolonged fMRI scanning sessions where the only instruction given is to close the eyes and do nothing. It has been recognized in recent years that resting state activity is implicated in a wide variety of brain function. While certain networks of brain areas have d...

In classification, semisupervised learning usually involves a large amount of unlabeled data with only a small number of labeled data. This imposes a great challenge in that it is difficult to achieve good classification performance through labeled data alone. To leverage unlabeled data for enhancing classification, this article introduces a large margin semisupervised learning method within th...

In this paper, we address the question of what kind of knowledge is generally transferable from unlabeled text. We suggest and analyze the semantic correlation of words as a generally transferable structure of the language and propose a new method to learn this structure using an appropriately chosen latent variable model. This semantic correlation contains structural information of the languag...

In this work we introduce a new approach to co-classification, i.e. the task of jointly classifying multiple, otherwise independent, data samples. The method we present, named CoConut, is based on the idea of adding a regularizer in the label space to encode certain priors on the resulting labelings. A regularizer that encourages labelings that are smooth across the test set, for instance, can ...

In this paper we propose to combine two powerful ideas, boosting and manifold learning. On the one hand, we improve ADABOOST by incorporating knowledge on the structure of the data into base classifier design and selection. On the other hand, we use ADABOOST’s efficient learning mechanism to significantly improve supervised and semi-supervised algorithms proposed in the context of manifold lear...

Recently, nonconvex regularization models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies φ in the total variation–type functional TV(u) := ∫ φ(|∇u(x)|) dx. In this paper, it is demonstrated that for typical choices of φ, functionals of this type pose several difficulties when extended to the entire spac...