Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Incremental Nonlinear Dimensionality Reduction by Manifold Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rapid and brief communication: Incremental locally linear embedding
Pattern Recognition
Incremental Laplacian eigenmaps by preserving adjacent information between data points
Pattern Recognition Letters
Computers in Biology and Medicine
Incremental manifold learning by spectral embedding methods
Pattern Recognition Letters
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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.