Abstract: Recently, manifold learning has been widely exploited in pattern recognition and data mining. Local tangent space alignment (LTSA) is a classical non-linear manifold learning method, which is efficient for non-linear dimensionality reduction. However, it fails to learn locally high curvature dataset. To address this problem, this paper describes the data set of the locally curvature by the given parameter and presents a new algorithm called locally minimal deviation space alignment (LMDSA). Considering the low-robust deficiencies in local tangent space, LMDSA can find the locally high curvature while computing locally minimal deviation spaces. The algorithm also reduces the probability of locally high curvature space with parameter control and the joint information between neighborhood information. Then the algorithm applies space alignment technique to reduce dimensionality. Besides the advantages above, LMDSA has the ability to learn sparse dataset. Extensive experiments on both synthetic manifold and real-world images indicate the efficiency of our algorithm. In synthetic manifold, LMDSA is compared with LTSA in two local high curvature datasets and one dataset with a hole. The experimental results show our algorithm learns correct manifold structure in low-dimension space. In sparse real-world datasets, LMDSA outperforms other algorithms in this paper.