一种新的局部空间排列算法

局部切空间排列算法(local tangent space alignment, LTSA)是一种经典的非线性流形学习方法，能够有效地对非线性分布数据进行降维，但它无法学习局部高曲率数据集.针对此问题，给出了描述数据集局部曲率的参数，并提出一种局部最小偏差空间排列(locally minimal deviation space alignment, LMDSA)算法.该算法考虑到局部切空间低鲁棒性的缺陷，在计算局部最小偏差空间的同时，能够发现数据的局部高曲率现象，通过参数控制及邻域间的连接信息，减少计算局部高曲率空间的可能，进而利用空间排列技术进行降维，手工流形及真实数据集的实验证实了该算法学习局部高曲率数据集的有效性.

A New Local Space Alignment Algorithm

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.