Algorithms.

Knowledge-leveraged transfer fuzzy C-means clustering (KL-TFCM)-c/-f

Inputs:	The target domain data set XT constituted by extracting texture features from the target texture image; the source domain data set XS composed of texture features from the referenced texture image; the cluster numbers CT and CS in the target and source domains, respectively; the convergence threshold ε; the fuzzifiers m, m1, m2 and parameters λ, β in Eq. (1), (5), or (12); and the maximum number of iterations max_iter
Outputs:	The eventual partitions on XT, i.e. the segmentation result of target texture image
Stage I: Knowledge extraction
Step I-1:	Set the iteration index t = 1, initialize the fuzzy memberships ${\mu }_{ij}^{(t)}$ in Eq. (1) and compute the cluster prototypes ${\overline{\mathbf{v}}}_i^{(t)}$, i = 1, …, CS, using Eq. (2) in the source domain XS;
Step I-2:	Compute the fuzzy memberships ${\mu }_{ij}^{(t+1)}$, i = 1, …, CS, j = 1, … NS, using Eq. (3);
Step I-3:	Compute the cluster prototypes ${\overline{\mathbf{v}}}_i^{(t+1)}$, i = 1, …, CS, using Eq. (2);
Step I-4:	If $\mid J_{\text{FCM}}^{(t+1)}-J_{\text{FCM}}^{(t)}\mid <\epsilon$ or t > max_iter, go to Step I-5; otherwise, set t = t + 1 and go to Step I-2;
Step I-5;	Step I-5: Set the cluster prototypes ${\mathbf{V}}_{\mathrm{S}}={\mathbf{V}}^{(t+1)}={[{\mathbf{v}}_1^{(t+1)},\dots ,{\mathbf{v}}_{C_{\mathrm{S}}}^{(t+1)}]}^{\mathrm{T}}$ in the source domain XS.
Stage II: Knowledge matching
Step II-1:	Set the iteration index t = 1, initialize the fuzzy memberships ${\mu }_{ij,\mathrm{T}}^{(t)}$ and the matching degrees $p_{jk}^{(t)}$ in Eq. (5), and compute the cluster prototypes ${\overline{\mathbf{v}}}_{j,\mathrm{T}}^{(t)}$, j = 1, …, CT, using Eq. (6) in the target domain XT;
Step II-2:	Compute the fuzzy memberships ${\mu }_{ij,\mathrm{T}}^{(t+1)}$, i = 1, …, NT, j = 1, …, CT, using Eq. (7);
Step II-3:	Compute the matching degrees $p_{jk}^{(t+1)}$, j = 1, …, CT, k = 1, …, CS, using Eq. (8);
Step II-4:	Compute the cluster prototypes ${\overline{\mathbf{v}}}_{j,\mathrm{T}}^{(t+1)}$, j = 1, …, CT, using Eq. (6);
Step II-5:	If $\mid J_{\text{KL}-\text{PM}}^{(t+1)}-J_{\text{KL}-\text{PM}}^{(t)}\mid <\epsilon$ or t > max_iter, go to Step II-6; otherwise, set t = t + 1 and go to Step II-2;
Step II-6:	Set the raw cluster prototypes ${\mathbf{V}}_{\mathrm{T}}^{\mathrm{r}}={\mathbf{V}}_{\mathrm{T}}^{(t+1)}={[{\mathbf{v}}_{1,\mathrm{T}}^{(t+1)},\dots ,{\mathbf{v}}_{C_{\mathrm{T}},\mathrm{T}}^{(t+1)}]}^{\mathrm{T}}$ and the final matching degrees ${\mathbf{P}}_{\mathrm{T}\&\mathrm{S}}={[p_{jk}^{(t+1)}]}_{C_{\mathrm{T}}\times C_{\mathrm{S}}}$;
Step II-5:	Generate the CT cluster representatives, ṼS = [ ṽ1,S, · · · , ṽCT,S]T, of the source domain as the final knowledge for the target domain, according to: Case-c: the crisp form, i.e. Eq. (9); Case-f: the flexible form, i.e. Eq. (10).
Stage III: Knowledge utilization
Step III-1:	Set the iteration index t = 1, initialize the cluster prototypes ${\mathbf{V}}_{\mathrm{T}}^{(t)}={\mathbf{V}}_{\mathrm{T}}^{\mathrm{r}}={[{\mathbf{v}}_{1,\mathrm{T}}^{\mathrm{r}},\cdots ,{\mathbf{v}}_{C_{\mathrm{T}},\mathrm{T}}^{\mathrm{r}}]}^{\mathrm{T}}$ in Eq. (12), and compute the fuzzy memberships ${\mu }_{ij,\mathrm{T}}^{(t)}$ using (14) in the target domain XT;
Step III-2:	Compute the cluster prototypes ${\overline{\mathbf{v}}}_{j,\mathrm{T}}^{(t+1)}$, j = 1, …, CT, using (13);
Step III-3:	Compute the fuzzy memberships ${\mu }_{ij,\mathrm{T}}^{(t+1)}$, i = 1, …, NT, j = 1, …, CT, using (14);
Step III-4:	If $\mid J_{\text{KL}-\text{TFCM}}^{(t+1)}-J_{\text{KL}-\text{TFCM}}^{(t)}\mid <\epsilon$ or t > max_iter, go to Step III-5; otherwise, t = t + 1 and go to Step III-2;
Step III-5:	The final memberships matrix UT in the target domain is achieved, i.e. ${\mathbf{U}}_{\mathrm{T}}={\mathbf{U}}_{\mathrm{T}}^{(t+1)}={[{\mu }_{ij,T}^{(t+1)}]}_{C_{\mathrm{T}}\times N_{\mathrm{T}}}$;
Step III-6:	Determine the eventual partitions on the target texture image according to the eventual memberships UT.