Algorithm 1.

Bi-organization Algorithm [10, Sec. 5.3]

Initialization

Input Dataset Z of features 𝒳 and observations 𝒴

1: Starting with features 𝒳

2:    Calculate initial metric $d_{𝒳}^{(0)}(x,x\prime )$

3:    Calculate initial flexible tree ${𝒯}_{𝒳}^{(0)}$.

Iterative analysis

Input Flexible tree on features ${𝒯}_{𝒳}^{(0)}$, weight function on tree folders W[i, i] = ω(ℐi)

4: for n ≥ 1 do

5:    Given tree ${𝒯}_{𝒳}^{(n)}$, calculate multiscale tree metric between observations $d_{{𝒯}_{𝒳}}^{(n)}(y,y\prime )={\Vert \mathbf{\text{WM}}(y,y\prime )\Vert }_1$

6:    Calculate flexible tree on the observations ${𝒯}_{𝒴}^{(n)}$.

7:    Repeat steps 5–6 for the features 𝒳 given ${𝒯}_{𝒴}^{(n)}$ and obtain ${𝒯}_{𝒳}^{(n+1)}$.

8: end for