Random Survival Forest for Censored Functional Data

Functional Random Survival Forest (FRSF) is an extended version of the Survival Random Forest (SRF) algorithm specifically developed to incorporate functional data as predictors in survival analysis. Inspired by a recent study, where a supervised classification method via a combined use of functional data analysis and tree-based methods is proposed, innovative functional splitting rules are introduced within FRSF by introducing censored functional data, enabling the generation of functional predictions even in the presence of complex or unknown relationships in the data. These novel splitting rules are carefully designed to capture the essen- tial features and patterns inherent in the functional predictors. By leveraging these functional indices, the predictive capabilities of the SRF algorithm are significantly enhanced, resulting in more accurate and reliable predictions. To generate the final prediction, the individual predictions are aggregated from all the trees in the forest. This ensemble approach leverages the collective knowledge of forecasts trees and incorporates the unique aspects of functional data, leading to improved performance in the prediction process.