Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Nonlinear manifold learning for dynamic shape and dynamic appearance
Computer Vision and Image Understanding
Incremental Laplacian eigenmaps by preserving adjacent information between data points
Pattern Recognition Letters
Supervised nonlinear dimensionality reduction for visualization and classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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A critical aspect of non-linear dimensionality reduction techniques is represented by the construction of the adjacency graph. The difficulty resides in finding the optimal parameters, a process which, in general, is heuristically driven. Recently, sparse representation has been proposed as a non-parametric solution to overcome this problem. In this paper, we demonstrate that this approach not only serves for the graph construction, but also represents an efficient and accurate alternative for out-of-sample embedding. Considering for a case study the Laplacian Eigenmaps, we applied our method to the face recognition problem. Experimental results conducted on some challenging datasets confirmed the robustness of our approach and its superiority when compared to existing techniques.