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.

Complexity of risk: Mixed methods approach to understanding youth risk and insecurity in post-conflict settings

In settings of intergroup conflict, identifying contextually-relevant risk factors for youth development in an important task. In Vukovar, Croatia, a city devastated during the war in former Yugoslavia, ethno-political tensions remain. The current study utilized a mixed method approach to identify two salient community-level risk factors (ethnic tension and general antisocial behavior) and related emotional insecurity responses (ethnic and non-ethnic insecurity) among youth in Vukovar. In Study 1, focus group discussions (N=66) with mother, fathers, and adolescents 11 to 15-years-old were analyzed using the Constant Comparative Method, revealing two types of risk and insecurity responses. In Study 2, youth (N=227, 58% male, M=15.88 SD=1.12 years old) responded to quantitative scales developed from the focus groups; discriminate validity was demonstrated and path analyses established predictive validity between each type of risk and insecurity. First, community ethnic tension (i.e., threats related to war/ethnic identity) significantly predicted ethnic insecurity for all youth (β=.41, p<.001). Second, experience with community antisocial behavior (i.e., general crime found in any context) predicted non-ethnic community insecurity for girls (β=.32, p<.05), but not for boys. These findings are the first to show multiple forms of emotional insecurity at the community level; implications for future research are discussed.