Robust linear programming discrimination of two linearly inseparable sets

Classifying ‘Drug-likeness' with Kernel-Based Learning Methods

“…We investigated methods that range from conventional decision trees, 15 Fishers Linear Discriminant 16 and Nearest Neighbor methods 17 to advanced learning techniques such as SVMs 5,7,8 and linear programming machines. 18,19 Contrary to Byvatov et al 12 we solely base our study on a Ghose-Crippen parametrization of the chemicals. 13 However, before feeding it into any of the learning machines we preprocess the GC descriptors by adding one and then computing the log.…”

“…18,19 To allow nonlinear classifications, one may nonlinearly map the examples into another feature space. In our experiments we used quadratic features (all first-and second-order monomials of the 120 input features).…”

An Introduction to Boosting and Leveraging

“…[167] and [27] indicated that AdaBoost computes hypotheses with large margins, if one continues iterating after reaching zero classification error. It is clear that the margin should be as large as possible on most training examples in order to minimize the complexity term in (17). If one assumes that the base learner always achieves a weighted training error t ≤ 1/2 − γ/2 with γ > 0, then AdaBoost generates a hypothesis with margin larger than γ/2 [167,27].…”

“…First we describe the DOOM approach [125] that uses a non-convex, monotone upper bound to the training error motivated from the margin-bounds. Then we discuss a linear program (LP) implementing a soft-margin [17,153] and outline algorithms to iteratively solve the linear programs [154,48,146].…”

“…, J} of J hypotheses. To find the coefficients w for the combined hypothesis f w (x) in (21), we extend the linear problem (30) and solve the following linear optimization problem (see also [17,154]), which we call the ν-LP problem:…”