H‐type indices with applications in chemometrics I: h‐multiple similarity index

Abstract

AbstractThe h‐index was originally proposed to measure the impact of individuals' scientific output, based on their number of publications and citations. In this paper, a variant of h‐index was proposed as a multiple similarity measure and its applications in chemometrics were studied. To measure the multiple similarity among a set of variables or objects, both the pairwise similarity and the coverage of high pairwise similarity across variables or objects were considered and measured with the suggested h‐multiple similarity index (HMSI). HMSI was defined as: based on the pairwise similarity (between [0,1]) among all objects in a set, if at most M% of all the pairwise similarity values is no less than M%, then the HMSI value of the batch will be M%. For applications, HMSI was used in three chemometrics problems: (1) to compare the stability of marker selection results by different classification models in metabonomics; (2) to measure the batch consistency of herbal high‐performance liquid chromatography (HPLC) fingerprints; and (3) to evaluate multivariate calibration models based on cross validation. The results indicate that HMSI is a simple, robust, and effective index to measure multiple similarity and useful in chemometrics applications.