Mathematical Programming in Data Mining

支持向量机（SVM）在各个领域的广泛问题中发挥了关键作用。最近，支持向量机已经成为数据挖掘中出现的问题的首选工具。该建议描述了支持向量机的一些方面，建议者希望进一步研究和贡献。其中包括：广义SVM（支持向量机的一般数学规划框架），无约束支持向量机（一个强凸最小化的SVM可解的快速有限方法），拉格朗日分类（支持向量机的无约束拉格朗日表示，导致一个非常简单的迭代方案，能够解决数百万数据点的分类问题）和减少数据分类（矩形核分类器，其特征在于只有1%的数据）。

ABSTRACT0138308Olvi MangssarianU of Wisconsin-MadisonSupport vector machines (SVMs) have played a key role in broad classes of problems arising in various fields. Much more recently, SVMs have become the tool of choice for problems arising in data mining. This proposal de-scribes some aspects of support vector machines that the proposer would like to study and contribute further to. These include: generalized SVMs (a gen-eral mathematical programming framework for SVMs), unconstrained SVMs (a strongly convex minimization reformulation of SVMs solvable by a fastfinite method), Lagrangian classification (an unconstrained Lagrangian rep-resentation of SVMs leading to an extremely simple iterative scheme capable of solving classification problems with millions of data points) and reduced data classification (a rectangular kernel classifier that is characterized by as little as 1% of the data).