eprintid: 4068 rev_number: 11 eprint_status: archive userid: 351 dir: disk0/00/00/40/68 datestamp: 2016-01-15 02:03:58 lastmod: 2021-08-27 17:14:42 status_changed: 2016-01-15 02:03:58 type: monograph metadata_visibility: show item_issues_count: 2 creators_name: Duarte Silva, A.P. creators_name: Stam, A. creators_id: 1602 title: Second Order Mathematical Formulations Programming for Discriminant Analysis ispublished: pub internal_subjects: iis_met internal_subjects: iis_inn internal_subjects: iis_sys divisions: prog_mda abstract: This paper introduces a nonparametric formulation-based mathematical programming (MP) for solving the classification problem in discriminant analysis. This method differs from previously proposed MP-based models in that, even though the final discriminant function is linear in terms of the parameters to be estimated, the formulation is quadratic in terms of the predictor (attribute) variables. By including second order (i.e., quadratic and cross-product) terms of the attribute variables, the model is similar in concept to the usual treatment of multiple predictor variables in statistical methods such as Fisher's linear discriminant analysis, and allows an analysis of how including nonlinear terms and interaction affect the predictive ability of the estimated classification function. Using simulation experiments involving data conditions for which nonlinear classifiers are appropriate, the classificatory performance of this class of second order MP models is compared with that of existing statistical (linear and quadratic) and first order MP-based formulations. The results of these experiments show that the proposed formulation appears to be a very attractive alternative to previously introduced linear and quadratic statistical and linear MP-based classification methods. date: 1994 date_type: published publisher: RR-95-007. Reprinted from European Journal of Operational Research, 72:4-22 [1994]. iiasapubid: RP-95-007 iiasa_bibref: Reprinted from European Journal of Operational Research; 72:4-22 [1994] price: 10 creators_browse_id: 1588 full_text_status: public monograph_type: research_reprint publication: European Journal of Operational Research volume: 72 place_of_pub: IIASA, Laxenburg, Austria pagerange: 4-22 pages: 22 refereed: TRUE coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Duarte Silva, A.P. & Stam, A. (1994). Second Order Mathematical Formulations Programming for Discriminant Analysis. IIASA Research Report (Reprint). IIASA, Laxenburg, Austria: RR-95-007. Reprinted from European Journal of Operational Research, 72:4-22 [1994]. document_url: https://pure.iiasa.ac.at/id/eprint/4068/1/RR-95-07.pdf