Ordinal-on-Function Dimensionality Reduction

In this communication, we tackle the challenge of dimensionality reduction of high dimensional objects, such as functional profiles, while maximizing the predictive power of an ordinal target variable. This issue is particularly important in sensor-driven decision-making processes, where the observable signal displays complexity and the aim is to evaluate a multi-level (ordinal) variable such as the degree of deterioration, quality, risk or stress of an object of interest. We describe a recent method called functional-ordinal Canonical Correlation Analysis (foCCA, [5]), which allows to perform ordinal-on-function dimensionality reduction. FoCCA reduces the dimensionality of observable features while optimizing their ability to distinguish between consecutive levels of an ordinal target variable. Differently from existing dimensionality reduction tools for functional data, foCCA fully integrates the ordinal nature of the target variable: in this way, foCCA captures and represents the relative differences between consecutive levels of the ordinal target, while also explaining these differences through the functional features. Extensive simulations show that foCCA performs better than current state-of-the-art dimensionality reduction tools in prediction accuracy within the reduced feature space. In particular, foCCA both improved predictive power and enhanced interpretability compared to other approaches.