Definition
A similarity metric, also known as L1 norm, that calculates the distance between two high-dimensional vectors by summing the absolute differences of their coordinates. In RAG pipelines, it serves as an alternative to Euclidean distance for vector retrieval, often providing more robust performance in high-dimensional spaces where individual feature axes have independent significance.
Measures distance along a grid (taxicab geometry) rather than 'as the crow flies' (Euclidean) or by angle (Cosine).
"A taxi driver navigating a strictly rectangular city grid where diagonal shortcuts are impossible, forcing travel only along horizontal and vertical streets."
- L1 Norm(Mathematical Basis)
- Euclidean Distance (L2)(Alternative Metric)
- Vector Indexing(Context)
- Curse of Dimensionality(Theoretical Constraint)
Conceptual Overview
A similarity metric, also known as L1 norm, that calculates the distance between two high-dimensional vectors by summing the absolute differences of their coordinates. In RAG pipelines, it serves as an alternative to Euclidean distance for vector retrieval, often providing more robust performance in high-dimensional spaces where individual feature axes have independent significance.
Disambiguation
Measures distance along a grid (taxicab geometry) rather than 'as the crow flies' (Euclidean) or by angle (Cosine).
Visual Analog
A taxi driver navigating a strictly rectangular city grid where diagonal shortcuts are impossible, forcing travel only along horizontal and vertical streets.