Manifold Learning Algorithm Based on Modified Local Tangent Space Alignment

The Local Tangent Space Alignment (LTSA) is one of the popular manifold learning algorithms since it is straightforward to implementation and global optimal. However, LTSA may fail when high-dimensional observation data are sparse or non-uniformly distributed. To address this issue, a modified LTSA algorithm is presented. At first, a new L1 norm based method is presented to estimate the local tangent space of the data manifold. By considering both distance and structure factors, the proposed method is more accurate than traditional Principal Component Analysis (PCA) method. To reduce the bias of coordinate alignment, a weighted scheme based on manifold structure is then designed, and the detailed solving method is also presented. Experimental results on both synthetic and real datasets demonstrate the effectiveness of the proposed method when dealing with sparse and non-uniformly manifold data.