A Subspace-based Approach for Dimensionality Reduction and Important Variable Selection

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few important features, but they are limited due to the lack of interpretability and connectivity to actual decision making associated with each physical variable. Variable selection techniques, as an alternative, can maintain the interpretability, but they often involve a greedy search that is susceptible to failure in capturing important interactions or a metaheuristic search that requires extensive computations. This research proposes a new method that produces subspaces, reduced-dimensional physical spaces, based on a randomized search and leverages an ensemble of critical subspace-based models, achieving dimensionality reduction and variable selection. When applied to high-dimensional data collected from the failure prediction of a composite/metal hybrid structure exhibiting complex progressive damage failure under loading, the proposed method outperforms the existing and potential alternatives in prediction and important variable selection.