Nearest feature line (NFL) embedding (NFLE) is an eigenspace transformation algorithm based on the NFL strategy. Based on this strategy, the NFLE algorithm generates a low dimensional space in which the local structures of samples in the original high dimensional space are preserved. Though NFLE has successfully demonstrated its discriminative capability, the non-linear manifold structure cannot be structured more efficiently by linear scatters using the linear NFLE method. To address this, a general NFLE transformation, called fuzzy/kernel NFLE, is proposed for feature extraction in which kernelization and fuzzification are simultaneously considered. In the proposed scheme, samples are projected into a kernel space and assigned larger weights based on that of their neighbors according to their neighbors. In that way, not only is the non-linear manifold structure preserved, but also are the discriminative powers of classifiers increased. The proposed method is compared with various state-of-the-art methods to evaluate the performance by several benchmark data sets. From the experimental results, the proposed FKNFLE outperformed the other, more conventional, methods.