A Penalized Likelihood Method for Classification With Matrix-Valued Predictors
A Penalized Likelihood Method for Classification With Matrix-Valued Predictors
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DOI：
10.1080/10618600.2018.1476249
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发表时间：
2019-01-02
影响因子：
2.4
通讯作者：
Rothman, Adam J.
中科院分区：
文献类型：
--
作者：
Molstad, Aaron J.;Rothman, Adam J.
当预测变量为矩阵值时，我们提出了一种惩罚似然方法来拟合线性判别分析模型。我们同时估计的手段和精度矩阵，我们假设有一个克罗内克积分解。我们的惩罚鼓励对响应类别均值矩阵估计有相等的条目，也鼓励零精度矩阵估计。为了计算我们的估计量，我们使用分块坐标下降算法。为了更新响应类别均值矩阵对应的优化变量，我们使用交替最小化算法，该算法利用精度矩阵的克罗内克结构。我们表明，我们的方法可以在分类方面优于相关竞争对手，即使我们的建模假设被违反。我们分析了三个真实的数据集，以证明我们的方法的适用性。补充材料，包括实现我们方法的R包，可以在线获得。
We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method's applicability. Supplementary materials, including an R package implementing our method, are available online.