Multicategory Composite Least Squares Classifiers.
Multicategory Composite Least Squares Classifiers.
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DOI：
10.1002/sam.10081
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发表时间：
2010-08
影响因子：
1.3
通讯作者：
Scholl, Paul
中科院分区：
文献类型：
--
作者：
Park, Seo Young;Liu, Yufeng;Liu, Dacheng;Scholl, Paul
分类是一种非常有用的信息抽取统计工具。特别是，多类别分类在各种应用中很常见。虽然二进制分类问题被大量研究，扩展到多类别的情况下是少得多。鉴于现代统计问题的复杂性和数量的增加，期望具有能够处理具有高维度和具有大量类的问题的多类别分类器。此外，多范畴分类器还必须具有良好的理论性质。在文献中，存在几个不同版本的同时多类别支持向量机（SVM）。然而，对于大规模问题，尤其是具有大量类的问题，支持向量机的计算可能很困难。此外，SVM不能直接产生类概率估计。在这篇文章中，我们提出了一种新的有效的多类别复合最小二乘分类器（CLS分类器），它利用了一个新的复合平方损失函数。建议CLS分类器有几个重要的优点：高效的计算问题，大量的类，渐近一致性，处理高维数据的能力，和简单的条件类概率估计。我们的模拟和真实的例子证明了所提出的方法的竞争力的性能。
Classification is a very useful statistical tool for information extraction. In particular, multicategory classification is commonly seen in various applications. Although binary classification problems are heavily studied, extensions to the multicategory case are much less so. In view of the increased complexity and volume of modern statistical problems, it is desirable to have multicategory classifiers that are able to handle problems with high dimensions and with a large number of classes. Moreover, it is necessary to have sound theoretical properties for the multicategory classifiers. In the literature, there exist several different versions of simultaneous multicategory Support Vector Machines (SVMs). However, the computation of the SVM can be difficult for large scale problems, especially for problems with large number of classes. Furthermore, the SVM cannot produce class probability estimation directly. In this article, we propose a novel efficient multicategory composite least squares classifier (CLS classifier), which utilizes a new composite squared loss function. The proposed CLS classifier has several important merits: efficient computation for problems with large number of classes, asymptotic consistency, ability to handle high dimensional data, and simple conditional class probability estimation. Our simulated and real examples demonstrate competitive performance of the proposed approach.