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There is a very important problem that has not attracted sufficient attentionin academia, i.e., nonlinear field normalization citation counts at the paperlevel obtained using nonlinear field normalization methods cannot be added oraveraged. Unfortunately, there are many cases adding or averaging the nonlinearnormalized citation counts of individual papers that can be found in theacademic literature, indicating that nonlinear field normalization methods havelong been misused in academia. In this paper, we performed the following tworesearch works. First, we analyzed why the nonlinear normalized citation countsof individual papers cannot be added or averaged from the perspective oftheoretical analysis in mathematics: we provide mathematical proofs for thecrucial steps of the analysis. Second, we systematically classified theexisting main field normalization methods into linear and nonlinear fieldnormalization methods. The above two research works provide a theoretical basisfor the proper use of field normalization methods in the future, avoiding thecontinued misuse of nonlinear data. Furthermore, because our mathematical proofis applicable to all nonlinear data in the entire real number domain, ourresearch works are also meaningful for the whole field of data and informationscience.

The misuse of the nonlinear field normalization method: Nonlinear field normalization citation counts at the paper level cannot be added or averaged