The eigen values do give information as to energy, so if your selection criteria is simply to pick the linear component with the most energy, you can use PCA to

The eigen values do give information as to energy, so if your selection criteria is simply to pick the linear component with the most energy, you can use PCA to select that feature and extract it with the corresponding eigen vector. The MUSIC algorithm is a classic example. Edit: having now actually read the article, the case I mention falls into the author's test of (do linear combinations of my features make sense and have as much of a relationship to the target as the features themselves).