高维数据的多类顶点判别分析
Multicategory vertex discriminant analysis for high-dimensional data
摘要：
为了应对数据挖掘的挑战，判别分析作为统计学的一个重要分支不断发展。我们最近引入的顶点判别分析（VDA）方法非常适合处理多个类别和训练案例中过多的预测因子。本文探讨了一种同时进行分类和变量选择的VDA阐述。向VDA损失函数添加lasso（$\ell_1$ -范数）和欧几里德罚分可消除不必要的预测因子。Lasso罚分分别应用于每个预测因子系数; Euclidean罚分将单个预测因子的集体系数分组。有了这些惩罚，循环坐标下降加速了所有系数的估计。我们对模拟和基准真实数据的测试证明了惩罚VDA在高维环境中建模和预测的优点。
英文摘要：
In response to the challenges of data mining, discriminant analysis continues to evolve as a vital branch of statistics. Our recently introduced method of vertex discriminant analysis (VDA) is ideally suited to handle multiple categories and an excess of predictors over training cases. The current paper explores an elaboration of VDA that conducts classification and variable selection simultaneously. Adding lasso ($\ell_1$-norm) and Euclidean penalties to the VDA loss function eliminates unnecessary predictors. Lasso penalties apply to each predictor coefficient separately; Euclidean penalties group the collective coefficients of a single predictor. With these penalties in place, cyclic coordinate descent accelerates estimation of all coefficients. Our tests on simulated and benchmark real data demonstrate the virtues of penalized VDA in model building and prediction in high-dimensional settings.
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