Techniques originally devised for analyzing infeasible linear programs turn out to have many interesting and useful applications in data analysis. The problem of placing a hyperplane in an n-dimensional space to separate two categories as well as possible can be directly transformed into an instance of the MAX FS problem, so the algorithms of Chap. 7 can be applied. This is also identical to the problem of providing the initial training for a neural network. A related problem in statistics is determining the data depth of a point in an n-dimensional cloud of data points, defined as the smallest number of data points on one side of hyperplane through the point in question. This is again transformable to the MAX FS problem. Finally, arithmetic constraints are often used to check massive data sets such as census results. The rules themselves may be contradictory, and this can be checked via the methods of Chaps. 6 and 7.


Data Depth Hyperplane Placement Arithmetic Constraint Halfspace Depth Tukey Depth 
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© Springer Science+Business Media, LLC 2008

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