Unified Optimization Frameworks for Joint Retrieval, Clustering, and Classification in Large-Scale Information Systems

• Esteban Cárdenas

  Universidad de Pamplona, Avenida Los Almeces 301, Department of Intelligent Computing, Pamplona, Norte de Santander, Colombia

  Author

• Mauricio Villalba

  Universidad del Cauca, Carrera, Department of Advanced Information Engineering, Popayán, Cauca, Colombia

  Author

In operational settings, learned vector representations functions are rarely isolated: retrieval quality depends on semantic structure that is also useful for clustering, while classification objectives shape representation geometry in ways that can either help or harm nearest-neighbor search. This paper develops a unified optimization view of joint retrieval, clustering, and classification, treating them as coupled objectives acting on shared embeddings, shared prototypes, and shared normalization constraints. The framework models retrieval as a metric-consistent ranking risk, clustering as a structured assignment of embeddings to latent groups, and classification as a supervised risk over the same embedding space, with explicit mechanisms for partial labels, class imbalance, and continuously arriving data. A central contribution is an integrated objective with controllable coupling strengths that admits scalable training via stochastic gradient steps, block-coordinate updates, and constrained assignment solvers. The paper analyzes how coupling induces trade-offs in embedding anisotropy, prototype collapse, and calibration of decision boundaries, and it proposes stability conditions that keep retrieval neighborhoods consistent under clustering and classification updates. Practical system considerations are addressed, including approximate nearest-neighbor indexing, delayed index refresh, streaming updates, and distributed training. The resulting framework provides a principled route for designing joint learners that match the intertwined requirements of modern retrieval-centric information systems.

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