Hyperspectral images with an immense number of spectral bands provide abundant discriminant information for accurate land-cover classification in the remote sensing field. However, these narrow and adjacent bands contain a large amount of redundant information. Analyzing these images always requires a huge storage space with expensive computational costs. Furthermore, their high correlation coefficient would lead to the Hughes phenomenon, hindering the improvement of classification performance. We propose a linear semi-supervised hyperspectral feature extraction method L³ME to learn latent local manifold embeddings. Although labeled samples are beneficial to construct learning models, their number is always limited in real-world tasks. The motivation of this paper is to jointly enhance the contributions of labeled and unlabeled samples for learning local manifold structures of hyperspectral images. Features in labeled samples are extracted by two procedures, the adaptive patch alignment framework and integrated intraclass-interclass relationships, from different perspectives. The former aims to solve the problem of the uneven distribution of classes by introducing spectral angle based adaptive parameters. The latter aims to solve the problem of the uneven distribution of samples by constructing several adjacency graphs. The locality preserving projection is capable of preserving the local neighborhood structure of samples. A penalty for sparse regularization is cleverly integrated into the proposed linear discriminant objective function, which is optimized using a novel updating strategy. The convergence of L³ME is proved in detail and analyzed in this paper. Experiments on three typical hyperspectral datasets illustrate the effectiveness of the proposed method over some state-of-the-art techniques. The implementation of L³ME is available at https://github.com/biowby/L3ME.