Manhattan Distance (L1)

Manhattan distance, also called L1 distance, taxicab distance, or city-block distance, measures the sum of absolute element-wise differences between two vectors — visualized as the path a taxi would drive on a grid of city streets where only right-angle turns are allowed. L1 is less common in modern embedding-based retrieval than cosine or Euclidean, but it has specific niches in sparse vector retrieval, certain robustness-focused applications, and image hashing. The metric is computationally cheaper than Euclidean because it avoids the squaring and square-root operations, which matters for very high-throughput retrieval. L1 is also more robust to outliers in individual vector dimensions, an advantage in scenarios where a few dimensions may be noisy or corrupted. Most vector databases including Milvus, FAISS, and pgvector support L1 as an optional distance metric alongside L2 and cosine. AI governance teams adopting L1 document the choice as part of their embedding pipeline lineage and validate Recall@k against ground truth in the same way as for any other metric.

Manhattan distance support in Centralpoint: Centralpoint supports L1, L2, cosine, and other distance metrics across whatever vector backend you operate, all under one model-agnostic governance layer. Tokens are metered per skill, prompts stay local, and L1-based chatbots embed across portals through one line of JavaScript.


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