Data dimensionality reduction via linear embedding is a typical approach to economizing the computational cost of machine learning systems. In the context of sparse subspace clustering (SSC), this paper proposes a two-step neighbor identification scheme using linear neighborhood-preserving embedding. In the first step, a quadratically-constrained l1 -minimization algorithm is solved for acquiring the side subspace neighborhood information, whereby a linear neighborhood-preserving embedding is designed accordingly. In the second step, a LASSO sparse regression algorithm is conducted for neighbor identification using the dimensionality-reduced data. The proposed embedding design explicitly takes into account the subspace neighborhood structure of the given data set. Computer simulations using real human face data show that the proposed embedding not only outperforms other existing dimensionality-reduction schemes but also improves the global data clustering accuracy when compared to the baseline solution without data compression.