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The rapid expansion of biomedical publications creates challenges for organizing knowledge and detecting emerging trends, underscoring the need for scalable and interpretable methods. Common clustering and topic modeling approaches such as K-means or LDA remain sensitive to initialization and prone to local optima, limiting reproducibility and evaluation. We propose a reformulation of a convex optimization based clustering algorithm that produces stable, fine-grained topics by selecting exemplars from the data and guaranteeing a global optimum. Applied to about 12,000 PubMed articles on aging and longevity, our method uncovers topics validated by medical experts. It yields interpretable topics spanning from molecular mechanisms to dietary supplements, physical activity, and gut microbiota. The method performs favorably, and most importantly, its reproducibility and interpretability distinguish it from common clustering approaches, including K-means, LDA, and BERTopic. This work provides a basis for developing scalable, web-accessible tools for knowledge discovery.