Integer Programming Problem Formulation Essay Example for Free

Integer Programming Problem Formulation EssayThis show up is advantageous compared to SVMs with Gaussian kernels in that it provides a natural stoolion of kernel matrices and it directly minimizes the chip of butt functions. Traditional approaches for data tracki? cation , that are based on partitioning the data sets into two groups, perform peaked(predicate) for multi-class data classi? ca- tion problems. The proposed approach is based on the use of hyper-boxes for de? ning boundaries of the classes that include all or some of the points in that set. A mixed-integer programming model is developed Computer Scientist, Defence RD Org. , Min of Defence, Delhi-110054. emailemailprotected drdo. in, dhamija. emailprotected com, a k emailprotected com. Home- pagewww. geocities. com/a k dhamija/ for representing existence of hyper-boxes and their boundaries. In addition, the relationships among the discrete decisions in the model are stand for using propositional logic and then c onverted to their equivalent integer constraints using Boolean algebra. Image line of business Enhancement and Image Recon- struction are being used for extracting knowledge from satellite images of the battle? ld or an opposite(prenominal) terrains. This method has already been described in LP problem formulation in I semester assignment. Keywords Integer linear Programming ,Pattern Classi? cation ,Multi Class data classi? cation , Image Reconstruction ,radial basis function (RBF) classi? ers , sigmoid function , SVM , meat and propositional logic 1Pattern Classification Via Integer linear Programming Given the space in which objects to be classi? ed are represented, a classi? er partitions the space into dis- joint regions and associates them with dierent classes. If the underlying distribution is known, an best artition of the space can be obtained according to the Bayes decision rule. In practice, however, the underlying distribution is seldom known, and a learning algorith m has to generate a partition that is close to the optimal partition from the training data. The RCE network (1) is a learning algorithm that constructs a set of regions, e. g. , spheres, to represent each pattern class. It is roaring to see that, with only a few spheres, there is a great chance that the training hallucination will be high.With an excessively large number of spheres, however, the training error can be reduced, but at the expense of over? ting the data and degrading the performance on future data. equal problems also exist in the radial basis function (RBF) networks and multi-layer sigmoid function networks. Therefore, a intimately learning algorithm has to strike a delicate balance between the training error and the complexness of the model.Existing method actings Used Various existing methods like Simulated Annealing , Neural Networks , Genetic algorithms and other classi- ?cation methods of supervised as well as unsupervised learning are being used. 1. 2 Prop osed Method ILP Problem Formulation Given a set of training examples, the minimum sphere overing approach seeks to construct a minimum num- ber of spheres (3) to overlay the training examples cor- rectly. Let us denote the set of training examples by D = f(x1 y1) (xn yn)g where xi 2 Rd and yi 2 f? 1 1g For notational simplicity, we only consider the binary classi? cation problem. The depute is to ? nd a set of class-speci? c spheres S = S1 Sm such that xi 2 y(Sj)=yi Sj and xi =2 y(Sj )6=yi Sj 8i = 1 n (1) where each sphere Si is characterized by its center c(Si), its radius r(Si) and its class y(Si). An exam- ple xi is covered by a sphere Sj , i. e. , xi 2 Sj , if d(xi c(Sj)) r(Sj ).A set of spheres S that satis? es the conditions in Eqn. (1) is called a consistent sphere cover of the data D. A sphere cover is minimal if there exists no other consis- tent sphere cover with a smaller number of spheres. We restrict ourselves to constructing a consistent sphere cover with sph eres that are centered on training ex- amples, although in general spheres do not have to be centered on the training examples. In hunting lodge to mini- mize the number of spheres in the sphere cover S, each sphere in S should cover as many training examples as possible without covering a training example belonging to a dierent class.