Integer Programming Problem Formulation
ILP Problem Formulation
Ajay Kr. Dhamija (N-1/MBA PT 2006-09)
Abstract
Integer linear programming is a very important class of problems, both algorithmically and combinatori- ally.Following are some of the problems in computer
Science ,relevant to DRDO, where integer linear Pro- gramming can be e®ectively used to ¯nd optimum so- lutions. 1. Pattern Classi¯cation
2. Multi Class Data Classi¯cation
3. Image Contrast Enhancement
Pattern Classi¯cation is being extensively used for automatic speech recognition, classi¯cation of text into several categories (e.g. spam/non-spam email messages), the automatic recognition of handwritten words, or the automatic recognition of images of human faces .I present here ,a minimum sphere cov- ering approach to pattern classi¯cation that seeks to construct a minimum number of spheres to represent the training data and formulate it as an integer programming problem. Using soft threshold functions, we can further derive a linear programming problem whose solution gives rise to radial basis function
(RBF) classi¯ers and sigmoid function classi¯ers. In contrast to traditional RBF and sigmoid function networks, in which the number of units is speci-
¯ed a priori, this method provides a new way to construct RBF and sigmoid function networks that explicitly minimizes the number of base units in the resulting classi¯ers. This approach is advantageous compared to SVMs with Gaussian kernels in that it provides a natural construction of kernel matrices and it directly minimizes the number of basis functions.
Traditional approaches for data classi¯cation , that are based on partitioning the data sets into two groups, perform poorly 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 R&D
Ajay Kr. Dhamija (N-1/MBA PT 2006-09)
Abstract
Integer linear programming is a very important class of problems, both algorithmically and combinatori- ally.Following are some of the problems in computer
Science ,relevant to DRDO, where integer linear Pro- gramming can be e®ectively used to ¯nd optimum so- lutions. 1. Pattern Classi¯cation
2. Multi Class Data Classi¯cation
3. Image Contrast Enhancement
Pattern Classi¯cation is being extensively used for automatic speech recognition, classi¯cation of text into several categories (e.g. spam/non-spam email messages), the automatic recognition of handwritten words, or the automatic recognition of images of human faces .I present here ,a minimum sphere cov- ering approach to pattern classi¯cation that seeks to construct a minimum number of spheres to represent the training data and formulate it as an integer programming problem. Using soft threshold functions, we can further derive a linear programming problem whose solution gives rise to radial basis function
(RBF) classi¯ers and sigmoid function classi¯ers. In contrast to traditional RBF and sigmoid function networks, in which the number of units is speci-
¯ed a priori, this method provides a new way to construct RBF and sigmoid function networks that explicitly minimizes the number of base units in the resulting classi¯ers. This approach is advantageous compared to SVMs with Gaussian kernels in that it provides a natural construction of kernel matrices and it directly minimizes the number of basis functions.
Traditional approaches for data classi¯cation , that are based on partitioning the data sets into two groups, perform poorly 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 R&D
References: 45:3541, 1982. M. R. Completeness. Freeman, New York, NY, 1979.