Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Incremental alignment manifold learning
Journal of Computer Science and Technology - Special issue on natural language processing
Object tracking using learned feature manifolds
Computer Vision and Image Understanding
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A number of manifold learning algorithms have been recently proposed, including locally linear embedding (LLE). These algorithms not only merely reduce data dimensionality, but also attempt to discover a true low dimensional structure of the data. The common feature of the most of these algorithms is that they operate in a batch or offline mode. Hence, when new data arrive, one needs to rerun these algorithms with the old data augmented by the new data. A solution for this problem is to make a certain algorithm online or incremental so that sequentially coming data will not cause time consuming recalculations. In this paper, we propose an incremental version of LLE and experimentally demonstrate its advantages in terms of topology preservation. Also, compared to the original (batch) LLE, the incremental LLE needs to solve a much smaller optimization problem.