Algorithm 1 Warm-Started ADMM for the Convex Clustering Problem (1)
Initialize l = 0, λl = ϵ, V(0) = Z(0) = DX
Repeat until ∥V(k)∥=0:
•  Repeat until convergence:
(i) U(K+1) = L−T L−1 (X + DT (V(k) − Z(k)))
(ii) V(k+1) = proxλlp(·;w,q) (DU(k+1) + Z(k))
(iii) Z(k+1) = Z(k) + DU(k+1) − V(k+1)
(iv) k := k + 1
•  Store U λl = U(k)
• Update regularization: l := l + 1 ; λl := λl−1 * t
Return {U λ} as the regularization path