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**1 - 2**of**2**### An Evaluation of Discrete Support Vector Machines for Cost-Sensitive Learning

"... Abstract — The problem of cost-sensitive learning involves classification analysis in scenarios where different error types are associated with asymmetric misclassification costs. Business applications and problems of medical diagnosis are prominent examples and pattern recognitions techniques are r ..."

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Abstract — The problem of cost-sensitive learning involves classification analysis in scenarios where different error types are associated with asymmetric misclassification costs. Business applications and problems of medical diagnosis are prominent examples and pattern recognitions techniques are routinely used to support decision making within these fields. In particular, support vector machines (SVMs) have been successfully applied, e.g. to evaluate customer credit worthiness in credit scoring or detect tumorous cells in bio-molecular data analysis. However, ordinary SVMs minimize a continuous approximation for the classification error giving similar importance to each error type. While several modifications have been proposed to make SVMs cost-sensitive the impact of the approximate error measurement is normally not considered. Recently, Orsenigo and Vercellis introduced a discrete SVM (DSVM) formulation [1] that minimize misclassification errors directly and overcomes possible limitations of an error proxy. For example, DSVM facilitates explicit cost minimization so that this technique is a promising candidate for cost-sensitive learning. Consequently, we compare DSVM with a standard procedure for cost-sensitive SVMs and investigate to what extent improvements in terms of misclassification costs are achievable. While the standard SVM performs remarkably well DSVM is found to give yet superior results. T I.

### An Interval-Pivoting Algorithm for the Uniform-Bound Interval-Flow Transportation Problem

, 2004

"... Presented herein is a new class of network flow models, interval-flow networks, in which the flow on an arc may be required to be either zero or within a specified range. The addition of such conditional lower bounds creates a mixed-integer program that captures such well-known restric-tions as mini ..."

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Presented herein is a new class of network flow models, interval-flow networks, in which the flow on an arc may be required to be either zero or within a specified range. The addition of such conditional lower bounds creates a mixed-integer program that captures such well-known restric-tions as minimum load sizes, minimum class enrollments, and minimum capacity utilization in telecommunications network spans. This paper describes the mathematical properties of interval-flow net-works as the basis for an efficient new heuristic approach that incorporates the conditional bounds into the simplex pivoting process and exploits the efficient, specialized pure-network simplex technologies. The algorithm is applied to interval-flow transportation problems with a uniform condi-tional lower bound and tested on problems with up to 5000 nodes and 10,000 arcs. Empirical comparisons with CPLEX demonstrate the ef-fectiveness of this methodology, both in terms of solution quality and processing time.