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By applying PCA we get a set of basis vectors,.
Empirical mode decomposition is a time-series analysis method that extracts a custom set of basis functions to describe the vibratory response of a system.
HSH are derived from spherical harmonics (SH) as an alternative set of basis functions on the unit sphere that are particularly aimed at non-negative function values.
A Galerkin formulation is derived by projecting the governing equations on a polynomial set of basis functions, which is constructed using the Gram Schmidt algorithm.
Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient.
Principal components were extracted from these average histograms providing a set of basis functions used to analyze stability of the response within and between sessions.
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While classical spectral methods utilize predetermined set of basis-functions (e.g., DFT, DCT) for representing the signal, sparse sensing methods, compute the set of basis-functions, which results in the sparsest representation of the signal, i.e., most coefficients of the signal's representation are zeros.
Finally, we define the concept of an expression program as a set of basis vectors spanning η.
The set of basis-functions is referred to as dictionary, where each element in the dictionary is an atom.
The method consists of numerically developing a set of basis solutions characterized by new dependent variables which are slowly varying.
This approach can be interpreted as a variant of the spectral method with a truncated set of basis functions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com