Improved local tangent space alignment algorithm
一种改进的局部切空间排列算法

As one of the classical manifold learning algorithms, LTSA algorithm can yield low-dimensional embedding coordinates from high-dimensional space effectively. Tangent space plays a central role in LTSA algorithm by projecting each neighborhood into the tangent space to obtain the local coordinates. However, in practice, LTSA algorithm takes the space which spanned by principal components of the sample covariance matrix of the neighborhood as the tangent space of the point. This paper presented a more rigorous method to calculate tangent space, that the neighborhood matrix of data points was centralized in accordance with the data point itself. By mathematical deduction, it proved that, under the approximation of first order Taylor, the space attained by our method is even the tangent space of data points itself. Based on this method, it proposed an improved local tangent space alignment algorithm. The effectiveness and stability of this algorithm are further confirmed by some experiments. Moreover, the proposed algorithm has no increase in the computational complexity.