This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are adapted to learn dynamic decision rules with respect to the index variable. In particular, we propose and study a new supervised dimension reduction method employing kernel smoothing to identify the optimal subspace, and provide a comprehensive examination of this approach for both linear discriminant analysis and quadratic discriminant analysis. We illustrate the effectiveness of the proposed methods through numerical simulations and real data examples. The results show considerable improvements in classification accuracy and computational efficiency. This work contributes to the field by offering a robust and adaptive solution to the challenges of scalability and non-staticity in high-dimensional data classification.

翻译：本文提出了一种新颖的高维空间动态分类框架，旨在解决类别分布随时间或其他索引变量演变的特性。传统判别分析技术经过改进，能够学习关于索引变量的动态决策规则。特别地，我们提出并研究了一种新的监督降维方法，该方法采用核平滑来识别最优子空间，并对线性判别分析和二次判别分析中该方法的运用进行了全面考察。通过数值模拟和实际数据示例，我们展示了所提方法的有效性。结果表明，该方法在分类准确率和计算效率方面均有显著提升。本研究通过为高维数据分类中的可扩展性和非静态性挑战提供稳健且自适应的解决方案，对该领域作出了贡献。