Algorithm 2.

Substructural Joint Probability Distribution Adaptation with Bi-Projection Metrix (SSJPDA-BPM)

Input:      XS and Xt, source and target domain      feature matrices;      YS, source domain one-hot coding label      matrix;      μ, trade-off parameter;      λ, regularization parameter;      T, number of iterations;   Output:      ${\widehat{Y}}_t$, estimated target domain labels.   Begin:      Use EM for GMM, cluster each class      data in the source to obtain      $\{Z_S,Y_S^{\prime }\}={\{({\text{z}}_{s,i},y_{s,i}^{\prime })\}}_{i=1}^{k_s}$, and cluster the      unlabeled data in target domain      to obtain $Z_t={\{z_{t,j}\}}_{j=1}^{k_t}$;      Compute cost matrix C and coupling      matrix π using Eq. 3 and Eq. 4      respectively;      Compute the weights of source      substructures $w_s={\text{π}}_1^{*}{1}_{k_t}$ and target      substructures $w_t=\frac{1_{k_t}}{k_t}$      for n = 1, …, T do         Construct the joint probability         matrix R in Eq. 17         Solve the generalized         eigen-decomposition problem in         Eq. 18 and Eq. 19, and select the p         trailing eigenvectors to construct         the projection matrix As and At;         Train a classifier f on $A_s^{\text{T}}{Z}_s$         and applied to $A_t^{\text{T}}{Z}_t$ to obtain         ${\widehat{Y}}_t^{\prime }={\{y_{t,j}^{\prime }\}}_{j=1}^{k_t}$ which is the label matrix         of substructure in target domain         $Z_t={\{z_{t,j}\}}_{j=1}^{k_t}$      End for      For each substructure zt,j, assign its      label $y_{t,j}^{\prime }$ to all samples it contains,      and gets ${\widehat{Y}}_t={\{y_{t,j}\}}_{j=1}^{n_t}$   End