Maximum margin clustering was proposed lately and has shown promising performance in recent studies [1, 2]. It extends the theory of support vector machine to unsupervised learning. Despite its good performance, there are three major problems with maximum margin clustering that question its efficiency for real-world applications. First, it is computationally expensive and difficult to scale to large-scale datasets because the number of parameters in maximum margin clustering is quadratic in the number of examples. Second, it requires data preprocessing to ensure that any clustering boundary will pass through the origins, which makes it unsuitable for clustering unbalanced dataset. Third, it is sensitive to the choice of kernel functions, and requires external procedure to determine the appropriate values for the parameters of kernel functions. In this paper, we propose "generalized maximum margin clustering" framework that addresses the above three problems simultaneously.

We establish a general oracle inequality for clipped approximate minimizers of regularized empirical risks and apply this inequality to support vector machine (SVM) type algorithms. We then show that for SVMs using Gaussian RBF kernels for classification this oracle inequality leads to learning rates that are faster than the ones established in [9]. Finally, we use our oracle inequality to show that a simple parameter selection approach based on a validation set can yield the same fast learning rates without knowing the noise exponents which were required to be known a-priori in [9].

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation withvarious interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

We consider the problem of detecting humans and classifying their pose from a single image. Specifically, our goal is to devise a statistical model that simultaneously answerstwo questions: 1) is there a human in the image?

We consider the task of tuning hyperparameters in SVM models based on minimizing a smooth performance validation function, e.g., smoothed k-fold cross-validation error, using nonlineaI optimization techniques.

VM) attempt to learn low-density separators by maximizing the margin over labeled and unlabeled examples. The associated optimizationproblem is non-convex.

Maximum margin clustering was proposed lately and has shown promising performance in recent studies [1, 2]. It extends the theory of support vector machineto unsupervised learning. Despite its good performance, there are three major problems with maximum margin clustering that question its efficiency for real-world applications. First, it is computationally expensive anddifficult to scale to large-scale datasets because the number of parameters in maximum margin clustering is quadratic in the number of examples. Second, it requires data preprocessing to ensure that any clustering boundarywill pass through the origins, which makes it unsuitable for clustering unbalanced dataset. Third, it is sensitive to the choice of kernel functions, and requires external procedure to determine the appropriate values for the parameters of kernel functions. In this paper, we propose "generalized maximum margin clustering" framework that addresses the above three problems simultaneously.

The theoretical understanding of support vector machines (SVMs) and related kernel-based methods has been substantially improved in recent years.

This paper proposes a PAC-Bayes bound to measure the performance of Support Vector Machine (SVM) classifiers. The bound is based on learning a prior over the distribution of classifiers with a part of the training samples. Experimental work shows that this bound is tighter than the original PAC-Bayes, resulting in an enhancement of the predictive capabilities of the PAC-Bayes bound. In addition, it is shown that the use of this bound as a means to estimate the hyperparameters of the classifier compares favourably with cross validation in terms of accuracy of the model, while saving a lot of computational burden.