Authors - Sachin Kumar Abstract - E-commerce search engines rely on Query Expansion (QE) to bridge the semantic gap between user queries and product catalogs, but expansion can induce query drift, where retrieved results diverge from the user’s original intent. Evaluating QE on novel or out-of-distribution queries is fundamentally intractable under the standard Cranfield paradigm, which requires pre-compiled relevance judgments. This paper introduces the Generalized Authority-Hub Score (GAHS), an unsupervised evaluation metric that repurposes the product catalog’s relational structure— modeled as a product graph—as a dynamic proxy for retrieval quality. Drawing on the HITS algorithm, GAHS quantifies the topical coherence of a retrieved product set without requiring explicit relevance judgments. Using the Amazon ESCI dataset, we validate GAHS against MAP and nDCG@10 on a held-out seen query set, demonstrating strong rank-order agreement (Kendall’s τ = 1.0 with MAP, τ = 0.67 with nDCG@10). We further demonstrate its discriminative power on a disjoint unseen query set, and discuss an observed performance reversal between the two query sets and its implications for QE evaluation methodology.
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