Vector Norms: A Quick Guide | Built In
linear-algebravector-normsregularizationmachine-learning-math
Abstraction: L1, L2, Lp, and Linfinity vector norms explained for ML
Key points:
- A norm measures vector magnitude and must satisfy four properties: non-negativity, definiteness, triangle inequality, and homogeneity
- L1 (Manhattan) norm is the sum of absolute values; used in Lasso regression as a penalty term that promotes sparsity
- L2 (Euclidean) norm is the root of sum of squares; most common in ML; used in ridge regression; not robust to outliers because it squares components
- L-infinity (max) norm equals the absolute value of the largest component
- The general Lp norm generalizes all: substituting p=1, 2, or infinity recovers those three norms
- The L0 "norm" (not technically a norm — fails homogeneity) counts non-zero components and is used to model sparsity
Connections: Linear Algebra · Regularization · Machine Learning