Adaptive Basis Function

An Adaptive Basis Function is a basis function that ...

• Example(s):
  • Karhunen Loeve Expansion.
  • Eigenvectors of a Covariance Matrix, for the finite dimensional case.
  • …
• Counter-Example(s):
  • Fixed Basis Set.
• See: Gaussian Processes.

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References

2015

• https://www.quora.com/What-are-adaptive-basis-functions/answer/Allan-Steinhardt?srid=uuoZN
  • QUOTE: [Is is] a basis function that is built from the data presented. An example is the Karhunen Loeve expansion, or in the finite dimensional case the eigenvectors of a covariance matrix. This is in contrast to a fixed basis set, like say Fourier Coefficients. In compression there is often a trade between forming an adaptive basis (always more efficient in terms of dimension required) and a fixed basis, which is larger dimensionaly. In a fixed basis you dont need to store the basis, hence the trade.

2010

• (Jekabsons, 2010) ⇒ Gints Jekabsons. (2010). “Adaptive Basis Function Construction: An Approach for Adaptive Building of Sparse Polynomial Regression Models.” In: Machine learning. InTech,

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