Improving the normalization effect of mean-based method from the perspective of optimization: optimization-based linear methods and their performance

Abstract

Mean-based method may be the most popular linear method for field normalization of citation impact. However, the relatively good but not ideal performance of mean-based method, plus its being a special case of the general scaling method y = kx and the more general affine method y = kx + b, implies that more effective linear methods may exist. Under the idea of making the citation distribution of each field approximate a common reference distribution through the transformation of scaling method and affine method with unknown parameters k and b, we derived the scaling and affine methods under separate unweighted and weighted optimization models for 236 Web of Science subject categories. While the unweighted-optimization-based scaling and affine methods did not show full advantages over mean-based method, the weighted-optimization-based affine method showed a decided advantage over mean-based method along most parts of the distributions. At the same time, the trivial advantage of weighted-optimization-based scaling method over mean-based method indirectly validated the good normalization performance of mean-based method. Based on these results, we conclude that mean-based method is acceptable for general field normalization, but in the face of higher demands on normalization effect, the weighted-optimization-based affine method may be a better choice.