The task is to choose between LSH and HNSW for a vector database index, prioritizing semantic accuracy. The evaluation must assess how well each method retrieves semantically relevant results. Let’s evaluate the options.

Option A: Compare the cosine similarities of the embeddings of returned results against those of a representative sample of test inputs

Cosine similarity measures semantic closeness between vectors, directly assessing retrieval accuracy in a vector database. Comparing returned results’ embeddings to test inputs’ embeddings evaluates how well LSH or HNSW preserves semantic relationships, aligning with the priority.

Databricks Reference:"Cosine similarity is a standard metric for evaluating vector search accuracy"("Databricks Vector Search Documentation," 2023).

Option B: Compare the Bilingual Evaluation Understudy (BLEU) scores of returned results for a representative sample of test inputs

BLEU evaluates text generation (e.g., translations), not vector retrieval accuracy. It’s irrelevant for indexing performance.

Databricks Reference:"BLEU applies to generative tasks, not retrieval"("Generative AI Cookbook").

Option C: Compare the Recall-Oriented-Understudy for Gisting Evaluation (ROUGE) scores of returned results for a representative sample of test inputs

ROUGE is for summarization evaluation, not vector search. It doesn’t measure semantic accuracy in retrieval.

Databricks Reference:"ROUGE is unsuited for vector database evaluation"("Building LLM Applications with Databricks").

Option D: Compare the Levenshtein distances of returned results against a representative sample of test inputs

Levenshtein distance measures string edit distance, not semantic similarity in embeddings. It’s inappropriate for vector-based retrieval.

Databricks Reference: No specific support for Levenshtein in vector search contexts.

Conclusion: Option A (cosine similarity) is the correct approach, directly evaluating semantic accuracy in vector retrieval, as recommended by Databricks for Vector Search assessments.