An improved local tangent space alignment method for manifold learning

Principal component analysis (PCA) is widely used in recently proposed manifold learning algorithms to provide approximate local tangent spaces. However, such approximations provided by PCA may be inaccurate when local neighborhoods of the data manifold do not lie in or close to a linear subspace. Furthermore, the approximated tangent spaces can not fit the change in data distribution density. In this paper, a new method is proposed for providing faithful approximations to the local tangent spaces of a data manifold, which is proved to be more accurate than PCA. With this new method, an improved local tangent space alignment (ILTSA) algorithm is developed, which can efficiently recover the geometric structure of data manifolds even in the case when data are sparse or non-uniformly distributed. Experimental results are presented to illustrate the better performance of ILTSA on both synthetic data and image data.

Research highlights
► The proposed method is an improvement of the LTSA method.
► A new method for local tangent space approximation is proposed.
► It is more accurate than the widely used PCA approximation.
► The proposed method can deal with sparse or non-uniformly distributed data.