Global Optimization Methods for Extended Fisher Discriminant Analysis
Global Optimization Methods for Extended Fisher Discriminant Analysis
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发表时间：
2014-04
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通讯作者：
S. Iwata;Y. Nakatsukasa;A. Takeda
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作者：
S. Iwata;Y. Nakatsukasa;A. Takeda
Fisher判别分析（FDA）是二元分类的常见技术。我们称之为扩展的FDA的参数化扩展名是从强大优化的角度引入的。在这项工作中，WEST给出了扩展FDA的新概率相互作用。然后，我们删除用于解决扩展FDA引起的优化问题的算法：计算椭圆形的点和表面之间的距离。我们通过KKT点解决了这个问题，我们显示的是通过解决广义特征问题来获得的。我们通过利用矩阵结构来加快算法的速度，并证明全球最佳解决方案是具有最小Lagrange乘数的KKT点，可以将其作为最左边的特征值进行有效计算。数值实验说明了扩展FDA模型与我们的算法的效率和有效性。
The Fisher discriminant analysis (FDA) is a common technique for binary classication. A parametrized extension, which we call the extended FDA, has been introduced from the viewpoint of robust optimization. In this work, werst give a new probabilistic inter- pretation of the extended FDA. We then de- velop algorithms for solving an optimization problem that arises from the extended FDA: computing the distance between a point and the surface of an ellipsoid. We solve this problem via the KKT points, which we show are obtained by solving a generalized eigen- value problem. We speed up the algorithm by taking advantage of the matrix structure and proving that a globally optimal solution is a KKT point with the smallest Lagrange multiplier, which can be computed efficiently as the leftmost eigenvalue. Numerical exper- iments illustrate the efficiency and effective- ness of the extended FDA model combined with our algorithm.