Functional-Ordinal Canonical Correlation Analysis with Application to Data from Optical Sensors

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. Notably, foCCA does not require numerical optimization and is solved in closed form, ensuring computational efficiency and guaranteeing global optimality. FoCCA fully incorporates the ordinal nature of the target variable, embedding it in the Guttman space: 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, and a case study involving the prediction of antigen concentration levels from optical biosensor signals demonstrate the superior performance of foCCA.

本研究旨在解决基于功能轮廓型可观测特征预测目标序数变量的问题。该问题具有重要的实际价值，尤其在传感器系统驱动的决策场景中：当需要通过传感器采集的功能数据，评估某一流程的劣化程度、质量等级或风险阶段这类序数变量时，该问题的必要性尤为凸显。为此，我们提出一种基于功能数据分析的全新方法——函数序数典型相关分析（functional-ordinal Canonical Correlation Analysis，foCCA）。该方法可实现可观测特征的降维，同时最大化其区分序数目标变量相邻等级的能力。值得注意的是，foCCA无需数值优化，可通过闭式解直接求解，兼具计算高效性与全局最优性保证。foCCA充分融入目标变量的序数属性，将其嵌入古特曼空间（Guttman space）：这使得模型能够捕捉并表征序数目标变量相邻等级间的相对差异，同时通过功能特征对这些差异进行解释。大量仿真实验与一项基于光学生物传感器信号预测抗原浓度等级的案例研究均证明，foCCA的性能优于同类方法。