To determine the best distance metric for a retrieval task, start by setting up a controlled experiment using a labeled dataset. For example, if you’re working on a document retrieval system, curate a dataset where each query has a known set of relevant documents. Use an embedding model (e.g., BERT or a sentence transformer) to convert queries and documents into vectors. For each query, retrieve top-k results using both cosine similarity and Euclidean distance. Note that cosine requires normalized vectors (since it measures angular similarity), while Euclidean accounts for vector magnitude. Implement this with a library like FAISS or scikit-learn, ensuring identical preprocessing and model parameters for both metrics to isolate their impact.
Next, evaluate retrieval quality using precision@k and recall@k. For instance, calculate precision@10 as the proportion of relevant documents in the top 10 results, and recall@10 as the fraction of all relevant documents found in those 10. Aggregate these metrics across all queries and compare averages for both distance metrics. Use statistical tests (e.g., paired t-test) to determine if differences are significant. For example, in a movie recommendation task, you might find cosine achieves 85% precision@5 versus Euclidean’s 78%, suggesting cosine better captures user preferences. If results are close, consider domain-specific factors: cosine often works better for text (where direction matters more than magnitude), while Euclidean might suit scenarios where vector scale is meaningful, like image features.
Finally, analyze edge cases and practical constraints. If your dataset has varying document lengths (e.g., short tweets vs. long articles), cosine’s normalization might mitigate bias toward longer texts. Conversely, Euclidean could perform poorly here, as magnitude differences dominate. Also, test computational efficiency—Euclidean might be faster in some implementations due to simpler math, but the difference is often negligible. For example, a search system using user interaction data might prioritize cosine if it better aligns with semantic similarity, even if marginally slower. Document your findings and iterate: if neither metric suffices, explore alternatives like Manhattan distance or task-specific metrics (e.g., Jaccard for sparse data). The key is grounding the choice in empirical results tied to your specific data and use case.