Algorithm 3. BLSE

Input: labeled training data $X\in {\Re }^{\mathrm{D}\times n}$. Reduced dimension $d$.

Tradeoff parameters $\mathsf{\alpha }$, $\beta$ and $\gamma$.

1: Run Algorithm 1 to get the affinity weights matrix $Z$ of $X$.

2: Run Algorithm 2 to obtain the optimal projection matrix $V$.

Output: Projection matrix$V$.