Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Learning a Joint Manifold Representation from Multiple Data Sets
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
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Methods for nonlinear dimensionality reduction have been widely used for different purposes, but they are constrained to single manifold datasets. Considering that in real world applications, like video and image analysis, datasets with multiple manifolds are common, we propose a framework to find a low-dimensional embedding for data lying on multiple manifolds. Our approach is inspired on the manifold learning algorithm Laplacian Eigenmaps - LEM, computing the relationships among samples of different datasets based on an intra manifold comparison to unfold properly the data underlying structure. According to the results, our approach shows meaningful embeddings that outperform the results obtained by the conventional LEM algorithm and a previous close related work that analyzes multiple manifolds.