Hierarchical clustered multiclass discriminant analysis via cross-validation
提出一种基于层次聚类和交叉验证的线性判别分析方法，通过定义聚类间不相似度为交叉验证值来最小化误分类率，并开发快速近似算法，在人工和真实数据集上实现了高预测精度和快速计算。
Linear discriminant analysis (LDA) is a well-known method for multiclass classification and dimensionality reduction. However, in general, ordinary LDA does not achieve high prediction accuracy when observations in some classes are difficult to be classified. A novel cluster-based LDA method is proposed that significantly improves prediction accuracy. Hierarchical clustering is adopted, and the dissimilarity measure of two clusters is defined by the cross-validation (CV) value. Therefore, clusters are constructed such that the misclassification error rate is minimized. The proposed approach involves a heavy computational load because the CV value must be computed at each step of the hierarchical clustering algorithm. To address this issue, a regression formulation for LDA is developed and an efficient algorithm that computes an approximate CV value is constructed. The performance of the proposed method is investigated by applying it to both artificial and real datasets. The proposed method provides high prediction accuracy with fast computation from both numerical and theoretical viewpoints.