Algorithm 1. Discriminant Feature Extraction by SDA

Input: Drawn training voxel samples x1, …, xP, with their multi-resolution patch

signature f(xi) (i = 1, …, P) and anatomical label li.

Output: Projected signature $\widehat{\mathit{f}}\left({\mathit{x}}_i\right)(i=1,\dots ,P)$, and projection matrix M.

1. Compute the within class scatter matrix SW by Equation 3.

2. Perform affinity propagation to cluster voxel samples belonging to the prostate region into H1 subclasses and voxel samples belonging to the non-prostate region into H2 subclasses.

3. Compute the between class scatter matrix SB by Equation 4.

4. Perform eigen-analysis on (SW)−1SB to obtain its most significant eigenvectors forming matrix V, and diagonal matrix Λ containing the largest eigenvalues.

5. Let M = Λ−1/2VT.

6. Calculate the projected feature signature $\widehat{\mathit{f}}\left({\mathit{x}}_i\right)=\mathbf{M}\mathit{f}\left({\mathit{x}}_i\right)(i=1,\dots ,P)$.

7. Return $\widehat{\mathit{f}}\left({\mathit{x}}_i\right)(i=1,\dots ,P)$, and M.