Algorithm 2:

The ZIPFA cross-validation algorithm in tth fold

Matrix $A\in {ℝ}^{n\times m}$ is to be decomposed to κ factors.

Initialize:

(1) Let $\tilde{A}$ be the same matrix as A but all 0’s and elements corresponding to $I_d^{\left[t\right]}$ are replaced by the column mean of rest values;

(2) Apply SVD to ln $\left(\tilde{A}\right)$ to obtain the components Uold and Vold;

(3) Calculate relative row sum N without elements corresponding to $I_d^{\left[t\right]}$;

(4) Eliminate the elements with index $I_d^{\left[t\right]}$ in A(v) (or A(u)) and note down their locations. Cross out elements in N(v) (or N(u)) on the corresponding location.

Update:

This part remains the same as regular ZIPFA algorithm described before.

CV likelihood:

(5) Obtain Λ(fit) = U(final)V(final)⊤ and calculate P(fit) = −τΛ(fit).

(6) Use the distribution assumption in Section 2.1 to calculate the likelihood of elements in A with index $I_d^{\left[t\right]}$ and sum them up.