Application of Conic Optimization and Semidefinite Programming in Classification

In this paper, Conic optimization and semidefinite programming (SDP) are utilized and applied in classification problem. Two new classification algorithms are proposed and completely described. The new algorithms are; the Voting Classifier (VC) and the N-ellipsoidal Classifier (NEC). Both are built on solving a Semidefinite Quadratic Linear (SQL) optimization problem of dimension n where n is the number of features describing each pattern in the classification problem. The voting classifier updates usage of ellipsoids in separating N different classes instead of only binary classification by using a voting unit. The N-ellipsoidal classifier makes the separation by means of N separating ellipsoids each contains one of the N learning sets of the classes intended to be separated. Experiments are performed on some data sets from UCI machine learning repository. Results are compared with several wellknown classification algorithms, and the proposed approaches are shown to provide more accurate and less complex classification systems with competitive error rates.