Multivariate Optimization of k for k-Nearest-Neighbor Feature Selection With Dichotomous Outcomes: Complex...

Optimization of nearest-neighbor feature selection depends on the number of samples and features, the type of statistical effect, the feature scoring algorithm, and class imbalance. We recently reported a fixed-k for Nearest-neighbor Projected-Distance Regression (NPDR) that addresses each of these parameters, except for class imbalance. To remedy this, we parameterize our NPDR fixed-k by the minority class size (minority-class-k). We also introduce a class-adaptive fixed-k (hit-miss-k) to improve performance of Relief-based algorithms on imbalanced data. In addition, we present two optimization methods, including constrained variable-wise optimized k (VWOK) and a fixed-k derived with principal components analysis (kPCA), both of which are adaptive to class imbalance. Using simulated data, we show that our methods significantly improve feature detection across a variety of nearest-neighbor feature scoring metrics, and we demonstrate superior performance in comparison to random forest and ridge regression using consensus-nested cross-validation (cnCV) for feature selection. We applied cnCV to RNASeq expression data from a study of Major Depressive Disorder (MDD) using NPDR with minority-class-k, random forest, and cnCV-ridge regression for gene importance. Pathway analysis showed that NPDR with minority-class-k alone detected genes with clear relevance to MDD, suggesting that our new fixed-k formula is an effective rule-of-thumb.