We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied directly or have poor performance due to the curse of dimensionality. To address this concern, we propose to project functional data onto one specific direction, and then a distance-weighted discrimination DWD classifier is built upon the projection score. The projection direction is identified through minimizing an empirical risk function that contains the particular loss function in a DWD classifier, over a reproducing kernel Hilbert space. Hence our proposed classifier can avoid overfitting and enjoy appealing properties of DWD classifiers. This framework is further extended to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate. In finite sample case, we demonstrate that the proposed classifiers compare favorably with some commonly used functional classifiers in terms of prediction accuracy through simulation studies and a real-world application.

翻译：当我们试图借用古典分类师的力量来对功能数据进行分类时,我们遇到一个瓶颈。 主要问题是功能数据本质上是无限的维度, 因此古典分类师无法直接应用, 或由于维度的诅咒而表现不佳。 为了解决这一问题, 我们提议将功能数据投射到一个特定的方向上, 然后在投影分上建立远程加权歧视 DWD 分类师。 投影方向是通过将包含DWD分类师特定损失函数的经验性风险功能降到最低程度, 而不是复制内核的 Hilbert 空间。 因此, 我们提议的分类师可以避免 DWD 分类师的过度配置和享受有吸引力的特性。 这个框架进一步扩展, 以适应涉及 calar 共变的功能性数据分类问题 。 与先前的工作相比, 我们根据相对分类错误的分类率, 在有限的抽样案例中, 我们证明, 拟议的分类师在通过模拟研究和现实应用在预测准确性方面与一些常用的功能分类师比较。