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.