Nearest shrunken centroids via alternative genewise shrinkages

Nearest shrunken centroids (NSC) is a popular classification method for microarray data. NSC calculates centroids for each class and 'shrinks' the centroids toward 0 using soft thresholding. Future observations are then assigned to the class with the minimum distance between the observation and the (shrunken) centroid. Under certain conditions the soft shrinkage used by NSC is equivalent to a LASSO penalty. However, this penalty can produce biased estimates when the true coefficients are large. In addition, NSC ignores the fact that multiple measures of the same gene are likely to be related to one another. We consider several alternative genewise shrinkage methods to address the aforementioned shortcomings of NSC. Three alternative penalties were considered: the smoothly clipped absolute deviation (SCAD), the adaptive LASSO (ADA), and the minimax concave penalty (MCP). We also showed that NSC can be performed in a genewise manner. Classification methods were derived for each alternative shrinkage method or alternative genewise penalty, and the performance of each new classification method was compared with that of conventional NSC on several simulated and real microarray data sets. Moreover, we applied the geometric mean approach for the alternative penalty functions. In general the alternative (genewise) penalties required fewer genes than NSC. The geometric mean of the class-specific prediction accuracies was improved, as well as the overall predictive accuracy in some cases. These results indicate that these alternative penalties should be considered when using NSC.