Sign consistency for the linear programming discriminant rule
Sign consistency for the linear programming discriminant rule
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线性规划判别规则的符号一致性
DOI：
10.1016/j.patcog.2019.107083
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发表时间：
2020-04-01
影响因子：
8
通讯作者：
Bian，Wei
中科院分区：
文献类型：
--
作者：
Zhang，Zhen;Wang，Shengzheng;Bian，Wei
线性判别分析（LDA）是一种重要的数据分类模型。经典理论表明，LDA是贝叶斯一致的固定的数据维数和一个大的训练样本大小。然而，在高维环境下，当p ∈ N时，由于协方差矩阵和总体均值向量的估计不一致，LDA是困难的。最近，线性规划判别（LPD）规则被提出用于高维线性判别分析，基于稀疏性假设的判别函数。结果表明，LPD规则是贝叶斯一致的高维设置。本文进一步证明了在稀疏性假设下LPD规则是符号相容的。这种符号一致性保证了LPD规则能够为高维数据分类问题选择最优的判别特征。对合成数据和真实的数据的评价验证了LPD规则符号一致性的结果。
Linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionalitypand a large training sample sizen. However, in high-dimensional settings whenp≫n, LDA is difficult due to the inconsistent estimation of the covariance matrix and the mean vectors of populations. Recently, a linear programming discriminant (LPD) rule was proposed for high-dimensional linear discriminant analysis, based on the sparsity assumption over the discriminant function. It is shown that the LPD rule is Bayes consistent in high-dimensional settings. In this paper, we further show that the LPD rule is sign consistent under the sparsity assumption. Such sign consistency ensures the LPD rule to select the optimal discriminative features for high-dimensional data classification problems. Evaluations on both synthetic and real data validate our result on the sign consistency of the LPD rule.