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.

A Synthesis-free Directional Modulation Transmitter using Retrodirective Array

By modification of the classical retrodirective arrays (RDAs) architecture a directional modulation (DM) transmitter can be realized without the need for synthesis. Importantly, through analytical analysis and exemplar simulations, it is proved that, besides the conventional DM application scenario, i.e., secure transmission to one legitimate receiver located along one spatial direction in free space, the proposed synthesis-free DM transmitter should also perform well for systems where there are more than one legitimate receivers positioned along different directions in free space, and where one or more legitimate receivers exist in a multipath environment. None of these have ever been achieved before using synthesis-free DM arrangements.