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SAC
2006
ACM
14 years 1 months ago
The impact of sample reduction on PCA-based feature extraction for supervised learning
“The curse of dimensionality” is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity and classification error in high dimension...
Mykola Pechenizkiy, Seppo Puuronen, Alexey Tsymbal
ICCS
2007
Springer
14 years 1 months ago
Hessian-Based Model Reduction for Large-Scale Data Assimilation Problems
Assimilation of spatially- and temporally-distributed state observations into simulations of dynamical systems stemming from discretized PDEs leads to inverse problems with high-di...
Omar Bashir, Omar Ghattas, Judith Hill, Bart G. va...
NIPS
2001
13 years 9 months ago
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motiva...
Mikhail Belkin, Partha Niyogi
CVPR
2008
IEEE
14 years 9 months ago
Margin-based discriminant dimensionality reduction for visual recognition
Nearest neighbour classifiers and related kernel methods often perform poorly in high dimensional problems because it is infeasible to include enough training samples to cover the...
Hakan Cevikalp, Bill Triggs, Frédéri...
CVPR
2007
IEEE
14 years 9 months ago
Connecting the Out-of-Sample and Pre-Image Problems in Kernel Methods
Kernel methods have been widely studied in the field of pattern recognition. These methods implicitly map, "the kernel trick," the data into a space which is more approp...
Pablo Arias, Gregory Randall, Guillermo Sapiro