We address the problem of predicting a target ordinal variable based on observable features consisting of functional profiles. This problem is crucial, especially in decision-making driven by sensor systems, when the goal is to assess an ordinal variable such as the degree of deterioration, quality level, or risk stage of a process, starting from functional data observed via sensors. We purposely introduce a novel approach called functional-ordinal Canonical Correlation Analysis (foCCA), which is based on a functional data analysis approach. FoCCA allows for dimensionality reduction of observable features while maximizing their ability to differentiate between consecutive levels of an ordinal target variable. Unlike existing methods for supervised learning from functional data, foCCA fully incorporates the ordinal nature of the target variable. This enables the model to capture and represent the relative dissimilarities between consecutive levels of the ordinal target, while also explaining these differences through the functional features. Extensive simulations demonstrate that foCCA outperforms current state-of-the-art methods in terms of prediction accuracy in the reduced feature space. A case study involving the prediction of antigen concentration levels from optical biosensor signals further confirms the superior performance of foCCA, showcasing both improved predictive power and enhanced interpretability compared to competing approaches.

翻译：本文研究基于由功能曲线构成的可观测特征预测目标序数变量的问题。该问题在传感器系统驱动的决策过程中尤为重要，其目标是从传感器观测的功能数据出发，评估如过程劣化程度、质量等级或风险阶段等序数变量。我们提出了一种基于功能数据分析方法的新颖方法——功能-序数典型相关分析（foCCA）。foCCA能够在降低可观测特征维度的同时，最大化其区分序数目标变量连续层级的能力。与现有的功能数据监督学习方法不同，foCCA充分考虑了目标变量的序数特性。这使得模型能够捕捉并表征序数目标连续层级间的相对差异，同时通过功能特征解释这些差异。大量仿真实验表明，在降维特征空间中，foCCA在预测精度方面优于当前最先进的方法。一项通过光学生物传感器信号预测抗原浓度水平的案例研究进一步证实了foCCA的优越性能，与现有方法相比，其不仅提升了预测能力，还增强了模型的可解释性。