A Deeper Dive into Wavelet Models for Functional Data Analysis

[#1]

A Wavelet model is a type of basis function model that is useful for data that contain a lot of peaks. This option requires data to be on an evenly spaced grid. If data is not evenly spaced, a grid is automatically created before the wavelet routine.  JMP Pro Functional Data Explorer handles and creates reports for Wavelet models.

See how Wavelet models work, and why they work so well for modeling data with sharp peaks, like spectroscopy data. A demonstration is included at timestamp 7:03.

• Wavelet Models for Functional Data Analysis (11:43)

If you are not familiar with basis function models for FDA, consider viewing A Deeper Dive into Basis Function Expansion Models for Functional Data Analysis video.

[Vins]

Hi @gail_massari and @chris_gotwalt1 

Great deep dive into wavelets.

When running functional data analysis using wavelets, the FDE platforms devices the number of grid points to use. Is it possible to set a custom number of grid points or evaluate a range of grid points?

Thanks,

Vins

[gail_massari]

Hi @Vins I am copying Di Michelson @Di_Michelson :

Hi @gail_massari and @chris_gotwalt1 

Great deep dive into wavelets.

When running functional data analysis using wavelets, the FDE platforms devices the number of grid points to use. Is it possible to set a custom number of grid points or evaluate a range of grid points?

[Di_Michelson]

@Vins Thanks for your question. The way wavelet models work is to first expand the domain so the number of domain points is a power of two. Then it breaks up the domain into halves, then quarters, then eighths, and so on, until the domain is completely broken up - at the end, there is one domain point in each segment. So there really isn't a grid like in spline models, and there's not a way to adjust how many segments there are - it's all related to the number of observations per function.

[Vins]

Thanks @Di_Michelson for the clarification. 

Best wishes, Vins