Linear support vector machines (svms) have become popular for solving classification tasks due to their fast and simple online application to large scale data sets. However, many problems are not linearly separable. For these problems kernel-based svms are often used, but unlike their linear variant they suffer from various drawbacks in terms of computational and memory efficiency. Their respon...

Extending work of [14, 16, 26], we show there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable L-spaces or compact S-spaces. The model is one of the form PFA(S)[S], where S is a coherent Souslin tree.

We propose a mixture model for blind source separation and deconvolution with adaptive source densities. Data is modelled as a multivariate locally linear random process. We derive an expression for the asymptotic likelihood of a linear process segment, which allows us to formulate and optimize a mixture model via the EM algorithm. The mixture model is able to represent nonstationary (locally, ...

We present locally-linear learning machines (L3M) for multi-class classification. We formulate a global convex risk function to jointly learn linear feature space partitions and region-specific linear classifiers. L3M’s features such as: (1) discriminative power similar to Kernel SVMs and Adaboost; (2) tight control on generalization error; (3) low training time cost due to on-line training; (4...

We propose a method for non-linear data projection that combines Generative Topographic Mapping and Coordinated PCA. We extend the Generative Topographic Mapping by using more complex nodes in the network: each node provides a linear map between the data space and the latent space. The location of a node in the data space is given by a smooth nonlinear function of its location in the latent spa...

We study linear time temporal logics of multiple agents, where the temporal modalities are local. These modalities not only refer to local next-instants and local eventuality, but also global views of agents at any local instant, which are updated due to communication from other agents. Thus agentsalso reason about the future, present and past of other agents in the system. The models for these...