Algorithm 1. SCDMDA

Input: Dataset ${\mathit{X}}_{\mathit{S}}$ and ${\mathit{X}}_{\mathit{T}}$, subspace dimension $k$, parameters $\alpha$, $\beta$, ${\lambda }_1$, $\theta$, and ${\lambda }_2$, classifier KTELM, maximum number of iterations $T_{\max }$. Output: Projection matrix $P$ and target prediction ${\tilde{\mathit{Y}}}_T$. Step1: According to Equations (1) and (9), construct $\mathit{Q}$, $\mathit{G}$, and ${\mathit{M}}_0$, and set $S_w$ and $S_b$ to 0. Step2: Let $t=1$. Step3: Solve Equation (12) or Equation (14) to obtain the projection matrix $P$. Step4: Project ${\mathit{X}}_S$ and ${\mathit{X}}_T$ by $P$ into $k$-dimensional subspace to obtain ${\mathit{Z}}_S$ and ${\mathit{Z}}_T$. Step5: Learn a KTELM on $\{{\mathit{Z}}_S,{\mathit{Y}}_S\}$, and classify ${\mathit{Z}}_T$ to obtain the label set of the target domain data ${\tilde{\mathit{Y}}}_T$. Step6: Use $\{{\mathit{X}}_S,{\mathit{Y}}_S\}$ and $\{{\mathit{X}}_T,{\tilde{\mathit{Y}}}_T\}$, construct $M_c$, and solve $S_w$ and $S_b$ ($S_w^{\phi }$ and $S_b^{\phi }$ in the nonlinear case) according to Equations (2) and (3). Step7: Let $t\leftarrow t+1$. Step8: If $t\ge T_{\max }$ or ${\tilde{\mathit{Y}}}_T$ does not change, output $P$, otherwise, go to Step3.