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Classification with Axis-Aligned Rectangular Boundaries
Abstract
This chapter presents a new method for binary classification that classifies input data into two regions separated by axis-aligned rectangular boundaries. Given the number of rectangular regions to use, this algorithm automatically finds the best boundaries that are determined concurrently. The formulation of the optimization problem involves minimizing the sum of minimum functions. To solve this problem, the author introduces underestimate of the minimum function with piecewise linear and convex envelope, which results in mixed integer and linear programming. The author shows several results of the algorithm and compare the effects of each term in the objective function. Finally, the chapter demonstrates that the method can be used in image capturing application to determine the optimal scheme that minimizes the total readout time of pixel data.
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