Table 17 Search algorithm

● Input:

−initial partition $\{F_1^1,\dots ,F_l^1\}$

−Data set $\mathcal{F}$

● Iterations:

1. Use the SVD to find $\{V_1^1,\dots ,V_l^1\}$ by minimizing $e\left(F_i^1,V_i^1\right)$ for each i, and compute ${\Gamma }_1=\sum _{i}e\left(F_i^1,V_i^1\right)$;

2. Set j=1;

3. While${\Gamma }_j=\sum _{i}e\left(F_i^j,V_i^j\right)>e\left(\mathcal{F},\{V_1^j,\dots ,V_l^j\}\right)$

4. Choose a new partition $\left\{F_1^{j+1},\dots ,F_l^{j+1}\right\}$ that satisfies, $f\in F_k^{j+1}$ implies that $d\left(f,V_k^j\right)\le d\left(f,V_h^j\right)$, $h=1,\dots ,l$;

5. Use SVD to find and choose $\{V_1^{j+1},\dots ,V_l^{j+1}\}$, by minimizing $e\left(F_i^{j+1},V_i\right)$ for each i, and compute ${\Gamma }_{j+1}=\sum _{i}e\left(F_i^{j+1},V_i^{j+1}\right)$;

6. Increment j by 1, i.e., j→j + 1;

7. End while

● Output:

−$\{F_1^j,\dots ,F_l^j\}$ and $\{V_1^j,\dots ,V_l^j\}$.