Table 1.

Common notations used throughout this manuscript.

Symbol	Use	Meaning
X = {x1,...xN} ∈ RN×D	Eq. (1)	The target data set with N data instances and D dimensions
XT = {x1,T,...xNT,T} ∈ RNT × D	Eqs. (5) and (12)	The data set in the target domain with NT data instances and D dimensions
U = [μij]C×N	Eq. (1)	The C × N membership matrix with μij indicating the membership degree of xj(j = 1,..., N) belonging to cluster i(i = 1,…, C)
UT = [μij,T]CT×NT	Eqs. (5) and (12)	The generated CT ×NT membership matrix in the target domain with μij,T indicating the membership degree of xj(j = 1,..., NT) belonging to cluster i (i = 1,…, CT)
PT&S = [pjk]CT×CS	Eq. (5)	The matching degree matrix with pjk indicating the matching degree of the jth estimated cluster prototype in the target domain to the kth cluster prototype in the source domain; CT and CS denote the cluster numbers in the target and source domains respectively
V = [v1,···,vC]T	Eq. (1)	The cluster prototype matrix with vi = [vi1, ···, viD]T (i = 1,..., C) signifying the ith cluster prototype (centroid)
VT = [v1,T, ···, vCT,T]T	Eqs. (4),(5),(11), and (12)	The cluster prototype matrix in the target domain with vj,T = [vj1,T, ···, vjD,T]T (j = 1,..., CT) signifying the jth cluster prototype (centroid)
${\mathbf{V}}_{\mathrm{T}}^{\mathrm{r}}={[{\mathbf{v}}_{1,\mathrm{T}}^{\mathrm{r}},\cdots ,{\mathbf{v}}_{C_{\mathrm{T}},\mathrm{T}}^{\mathrm{r}}]}^{\mathrm{T}}$	Generated in the knowledge matching stage, and used in the knowledge utilization stage	The raw cluster prototypes in the target domain estimated by KL-PM with ${\mathbf{V}}_{j,\mathrm{T}}^{\mathrm{r}}={[v_{j1,\mathrm{T}}^{\mathrm{r}},\cdots ,v_{jD,\mathrm{T}}^{\mathrm{r}}]}^{\mathrm{T}}(j=1,\dots ,C_{\mathrm{T}})$ signifying the jth raw cluster prototype (centroid)
VS = [v1,S, ···, vCS,S]T	Eqs. (4),(5), and (11)	The cluster prototype matrix in the source domain with vk,S = [vk1,S, ···, vkD,S]T (k = 1,..., CS) signifying the kth cluster prototype (centroid)
ṼS = [ṽ1,S, ···, ṽCT,S]T	Eqs. (9)–(12); Generated in the knowledge matching stage, and used in the knowledge utilization stage	The employed cluster representatives from the source domain for the eventual knowledge utilization in the target domain with ṽ j,S = [ṽj1,S, ···, ṽjD,S]T (j = 1,..., CT) denoting the jth cluster representative in the source domain