Incremental Manifold Learning Via Tangent Space Alignment

Several algorithms have been proposed to analysis the structure of high-dimensional data based on the notion of manifold learning. They have been used to extract the intrinsic characteristic of different type of high-dimensional data by performing nonlinear dimensionality reduction. Most of them operate in a “batch” mode and cannot be efficiently applied when data are collected sequentially. In this paper, we proposed an incremental version (ILTSA) of LTSA (Local Tangent Space Alignment), which is one of the key manifold learning algorithms. Besides, a landmark version of LTSA (LLTSA) is proposed, where landmarks are selected based on LASSO regression, which is well known to favor sparse approximations because it uses regularization with l1 norm. Furthermore, an incremental version (ILLTSA) of LLTSA is also proposed. Experimental results on synthetic data and real word data sets demonstrate the effectivity of our algorithms.