Algorithm 2 — Initialization — Determinental Point Processes

Input: X ∈ ℝn×d, y ∈ {−1, +1}n (training signals), K (number of clusters), m (number of hyperplanes samples to draw)

Output: ${\mathbf{S}}^{-}\in {\left[0,1\right]}^{n^{-}\times K}$ (Initial Clustering Assignment)

• Randomly draw m pairs of negative (x−) and positive (x+) samples (with replacement): ${\{{\mathbf{x}}_i^{-},{\mathbf{x}}_i^{+}\}}_{i=1}^m$

• Obtain m hyperplanes by taking the difference between members of the same pair: ${\mathbf{u}}_i=({\mathbf{x}}_i^{+}-{\mathbf{x}}_i^{-})/{\Vert {\mathbf{x}}_i^{+}-{\mathbf{x}}_i^{-}\Vert }_2$

• Sample K hyperplanes ${\{{\mathbf{w}}_j^0\}}_{j=1}^K$ from ${\left\{{\mathbf{u}}_i\right\}}_{i=1}^m$ by Determinental Point Processes (Kulesza and Taskar, 2012)

• Set rows of S− such that $s_{i,\text{arg}{min}_j{\mathbf{w}}_j^{0^T}{\mathbf{x}}_i}=1$, otherwise set si,j = 0