Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

On the Virtualization of CUDA Based GPU Remoting on ARM and X86 Machines in the GVirtuS Framework

The astonishing development of diverse and different hardware platforms is twofold: on one side, the challenge for the exascale performance for big data processing and management; on the other side, the mobile and embedded devices for data collection and human machine interaction. This drove to a highly hierarchical evolution of programming models. GVirtuS is the general virtualization system developed in 2009 and firstly introduced in 2010 enabling a completely transparent layer among GPUs and VMs. This paper shows the latest achievements and developments of GVirtuS, now supporting CUDA 6.5, memory management and scheduling. Thanks to the new and improved remoting capabilities, GVirtus now enables GPU sharing among physical and virtual machines based on x86 and ARM CPUs on local workstations,computing clusters and distributed cloud appliances.