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A Unified Near-Optimal Estimator For Dimension Reduction in lα (0 < α ≤ 2) Using Stable Random Projections
Near-Optimal Estimator Dimension Reduction Stable Random Projections
2015/8/21
Many tasks (e.g., clustering) in machine learning only require the lα distances instead of the original data. For dimension reductions in the lα norm (0 < α ≤ 2), the method of stable random projectio...
Nonlinear Estimators and Tail Bounds for Dimension Reduction in l1 Using Cauchy Random Projections
dimension reduction l1 norm Johnson-Lindenstrauss (JL) lemma Cauchy random projections
2015/8/21
For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k D) whose entries are i.i.d. samples of ...
Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations
Mathematical Physics (math-ph) Analysis of PDEs (math.AP) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/11
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigati...
Reduction operators of variable coefficient semilinear diffusion equations with an exponential source
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ ar...
This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by...