Why L1 distance is called Manhattan distance — grid-like paths

Why the L1 unit ball is a diamond shape and the L2 unit ball is a circle

L1 norm: Manhattan distance, L2 norm: Euclidean distance

Why the curse of dimensionality makes nearest neighbor search unreliable

High-dimensional spaces increase distance ambiguity, reducing nearest neighbor search reliability

Write the formula for Mahalanobis distance

D^2 = (x - μ)^T Σ^(-1) (x - μ)

Why L1 regularization produces sparse solutions — the diamond corners touch axes

L1 regularization promotes sparsity by penalizing non-zero coefficients, effectively driving some to zero

Why proximal gradient descent is needed for L1 optimization

Proximal gradient descent handles non-differentiable L1 regularization, enabling sparse solutions

How does the curse of dimensionality affect the performance and accuracy of clustering algorithms in high-dimensional datasets?

High-dimensional data can lead to sparse clusters, reducing clustering accuracy due to increased distance between points