Algorithm 1. Procedure of LJELSR.

Input: Data matrix $\mathrm{X}$; Neighborhood size $q$; Balance parameters ${\alpha }_1{,\alpha }_2,\beta$; Dimensionality of embedding $k$; Feature selection number $l$. Output: Selected feature index set $\left\{{\mathrm{P}}_1{,\mathrm{P}}_2,\cdots {,\mathrm{P}}_m\right\}$

Stage one: Graph construction Construct the weight matrix $\mathrm{W}$; Compute the diagonal matrix $\mathrm{D}$, graph Laplacian matrix $\mathrm{L}$; Stage two: Alternative optimization, Initialize $\mathrm{U}=\tilde{\mathrm{U}}={\mathrm{I}}_{m\times m}$; Loop Update $\mathrm{Y}$ and fix $\mathrm{A}$, $\mathrm{L}$ by (19), Update $\mathrm{P}$ and fix $\mathrm{U}$, $\tilde{\mathrm{U}}$ by (17), Update $\mathrm{U}$, $\tilde{\mathrm{U}}$ and fix $\mathrm{P}$ by (12) and (13). until convergence Stage three: Feature selection