Sparse Discriminant Analysis
Sparse Discriminant Analysis
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DOI：
10.1198/tech.2011.08118
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发表时间：
2011-11-01
期刊：
影响因子：
2.5
通讯作者：
Ersboll, Bjarne
中科院分区：
文献类型：
--
作者：
Clemmensen, Line;Hastie, Trevor;Ersboll, Bjarne
我们考虑在高维环境中进行可解释分类的问题，其中特征的数量非常大，观测的数量有限。这种设置已经在化学计量学文献中得到了广泛的研究，最近在生物和医学应用中已经变得司空见惯。在这种情况下，传统的方法涉及在分类之前执行特征选择。我们提出了稀疏判别分析，一种方法，用于执行线性判别分析的稀疏性标准施加，使分类和特征选择同时进行。稀疏判别分析是基于线性判别分析的最佳评分解释，并且如果类之间的边界是非线性的或者如果每个类内存在子组，则可以扩展为通过高斯混合来执行稀疏判别。我们的建议还提供了低维的歧视性方向的意见。
We consider the problem of performing interpretable classification in the high-dimensional setting, in which the number of features is very large and the number of observations is limited. This setting has been studied extensively in the chemometrics literature, and more recently has become commonplace in biological and medical applications. In this setting, a traditional approach involves performing feature selection before classification. We propose sparse discriminant analysis, a method for performing linear discriminant analysis with a sparseness criterion imposed such that classification and feature selection are performed simultaneously. Sparse discriminant analysis is based on the optimal scoring interpretation of linear discriminant analysis, and can be extended to perform sparse discrimination via mixtures of Gaussians if boundaries between classes are nonlinear or if subgroups are present within each class. Our proposal also provides low-dimensional views of the discriminative directions.