FPCAdens object description

[nickf314]

Hi, is there a detailed description of the objects returned by the FPCAdens function available somewhere? I could not find this in the documentation. While I could venture a guess based on Petersen and Muller (2016), I wanted to be certain what I am observing prior to using the output. Apologies if this is already available somewhere and I have missed it. Thanks for the help!

[alexpete]

Hello, Thank you for your email and your valuable feedback. I was surprised to see that the function did not have a description of the values returned. This will be addressed in the next version. The outputs of FPCAdens are precisely those of the function FPCA from the fdapace package applied to the transformed densities. So, FPCAdens is merely an interface that first performs the log quantile density transformation then applies FPCA. The most useful output is the matrix of scores xiEst, the rows of which can be used as proxies for the input densities. Additionally, the functions CreateModeOfVarPlotLQ2D and GetFVE help to interpret the FPCA results in density space. Please don't hesitate to ask for further clarification. Best, Alex

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On Mon, Jan 27, 2025 at 8:22 AM nickf314 ***@***.***> wrote: Hi, is there a detailed description of the objects returned by the FPCAdens function available somewhere? I could not find this in the documentation. While I could venture a guess based on Petersen and Muller (2016), I wanted to be certain what I am observing prior to using the output. Apologies if this is already available somewhere and I have missed it. Thanks for the help! — Reply to this email directly, view it on GitHub <#2>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA4G7TOX3ZKSKNMQRHSWQUT2MZFL5AVCNFSM6AAAAABV6KYT72VHI2DSMVQWIX3LMV43ASLTON2WKOZSHAYTGMZRGQ4DOMY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[nickf314]

Thanks, Alex. This is helpful, and great work with this very useful package. One further question: Suppose that I want to back-transform the results of FPCAdens to the density space using a some number of functional components that is less than the total number of components provided by FPCAdens (in other words, estimate the original density space with some error). I see we have a MakeDENsample function that should assist.

Now, I interpret xiEst matrix as the scores in the LQD space, the phi matrix as the eigenfunctions in LQD space, and mu as the mean function in LQD space. I can take the inner product of xiEst and the transpose of phi, add mu, and this should provide me with the matrix needed for the MakeDENsample function. Does this generally sound like the correct use of MakeDENsample ?

[alexpete]

Yes, that's correct. In fact, that is precisely what GetFVE does - it reconstructs the densities using K components, for various K, then computes the reconstruction error under different metrics.

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On Mon, Jan 27, 2025 at 10:27 AM Nick ***@***.***> wrote: Thanks, Alex. This is helpful, and great work with this very useful package. One further question: Suppose that I want to back-transform the results of FPCAdens to the density space using a some number of functional components that is less than the total number of components provided by FPCAdens (in other words, estimate the original density space with some error). I see we have a MakeDENsample function that should assist. Now, I interpret xiEst matrix as the scores in the LQD space, the phi matrix as the eigenfunctions in LQD space, and mu as the mean function in LQD space. I can take the inner product of xiEst and the transpose of phi, add mu, and this should provide me with the matrix needed for the MakeDENsample function. Does this generally sound like the correct use of MakeDENsample ? — Reply to this email directly, view it on GitHub <#2 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA4G7TIGAQFFL3FHD5TIUYT2MZUADAVCNFSM6AAAAABV6KYT72VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDMMJWGQ2DANBZGM> . You are receiving this because you commented.Message ID: ***@***.***>

[nickf314]

Very helpful, thanks Alex.