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Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures.
Extension of range of functions
E. J. McShane · 1934
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Analytic extensions of differentiable functions defined in closed sets
H. Whitney · 1934
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The imbedding problem for Riemannian manifolds
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Approximation by superpositions of a sigmoidal function
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On the approximate realization of continuous mappings by neural networks
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Multilayer feedforward networks are universal approximators
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Approximation and estimation bounds for artificial neural networks
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Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
E. J. Candès, J. Romberg, and T. Tao · 2006
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A mathematical introduction to compressive sensing
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Measure theory and fine properties of functions
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Universal function approximation by deep neural nets with bounded width and relu activations
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