Similarity-based fuzzy clustering scientific articles: Potentials and challenges from mathematical and computational perspectives

Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data.This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution.While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -which contain approximately 70 million articles and a billion citations -poses significant challenges.We analyze potentials and challenges of the approach from both mathematical and computational perspectives.Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem's structure.Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.