Algorithm 1 — HYDRA

Input: X ∈ Rn×d, y ∈ {−1, +1}n (training signals), C (loss penalty), K (number of clusters/hyperplanes)

Output: W ∈ ℝd×K, b ∈ ℝ1×K (Classifier); ${\mathbf{S}}^{-}\in {\left[0,1\right]}^{n^{-}\times K}$ (Clustering Assignment)

Initialization: Initialize S− by Algorithm 2

Loop: Repeat until convergence (or a fixed number of iterations)

• Fix S− — Solve for W, b by weighted LIBSVM (sample weights set by Eq. A.2)

• Fix W, b — Solve for S− using Eq. A.1