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. Copyright © 2010 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 3: 272‐286, 2010

中文翻译：

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多类别复合最小二乘分类器。

分类是一种非常有用的信息提取统计工具。特别是，多类别分类在各种应用中都很常见。尽管对二元分类问题进行了大量研究，但对多类别情况的扩展却少得多。鉴于现代统计问题的复杂性和数量不断增加，希望拥有能够处理高维度和大量类问题的多类别分类器。此外，多类别分类器必须具有良好的理论特性。在文献中，存在多个不同版本的同步多类别支持向量机 (SVM)。然而，SVM 的计算对于大规模问题可能很困难，尤其是对于具有大量类的问题。此外，SVM 不能直接产生类概率估计。在本文中，我们提出了一种新颖的高效多类别复合最小二乘分类器（CLS 分类器），它利用了一种新的复合平方损失函数。所提出的 CLS 分类器有几个重要优点：对大量类问题的高效计算、渐近一致性、处理高维数据的能力以及简单的条件类概率估计。我们的模拟和真实示例证明了所提出方法的竞争性能。版权所有 © 2010 Wiley Periodicals, Inc. 统计分析和数据挖掘 3: 272‐286, 2010 它利用了一个新的复合平方损失函数。所提出的 CLS 分类器有几个重要优点：对大量类问题的高效计算、渐近一致性、处理高维数据的能力以及简单的条件类概率估计。我们的模拟和真实示例证明了所提出方法的竞争性能。版权所有 © 2010 Wiley Periodicals, Inc. 统计分析和数据挖掘 3: 272‐286, 2010 它利用了一个新的复合平方损失函数。所提出的 CLS 分类器有几个重要优点：对大量类问题的高效计算、渐近一致性、处理高维数据的能力以及简单的条件类概率估计。我们的模拟和真实示例证明了所提出方法的竞争性能。版权所有 © 2010 Wiley Periodicals, Inc. 统计分析和数据挖掘 3: 272‐286, 2010 我们的模拟和真实示例证明了所提出方法的竞争性能。版权所有 © 2010 Wiley Periodicals, Inc. 统计分析和数据挖掘 3: 272‐286, 2010 我们的模拟和真实示例证明了所提出方法的竞争性能。版权所有 © 2010 Wiley Periodicals, Inc. 统计分析和数据挖掘 3: 272‐286, 2010