Is it possible to do DFPCA + regular PCA together?

Question

Hello - I am working on a paper and I have a lot of individual data points for different items, but some of those points come from data series (e.g. values at different temperatures, wavelengths, etc). So far I've selected certain points from those data series based on typical conditions (e.g. room temperature), but it would definitely elevate the analysis if the entire data series for each could be used. I see the DFPCA option in the functional data analysis platform. However, maybe I'm being a dunce and completely missing it, and there's a way to do multiple data points and data series, and do PCA with all of it. Is this possible? I'd even be open to a JSL option. I don't know JSL though, so if it would take weeks for me to be able to get the code up, I unfortunately don't have that kind of time flexibility.

Thanks!

ehchandlerjr · Answer

@Mark_Bailey and @Jed_Campbell, thanks for responding!

So rereading my question, I don't think I explained the question well. I apologize about that. As a more concrete example, say I have a bunch of materials, and for each one I have molar weight, density across temperature, and optical absorption at different wavelengths. The former is a single data point and is the kind of data one would perform regular PCA on, while the latter two are functional data. However, you have two functional data series that use different x axes. My question is how would one perform PCA on all three of these together, or is it even possible?

Is there a reason you're using that rather than fitting a model to your data? In my experience, fitting a model (Red Triangle...Models) is usually the first step. Direct FPCA is certainly an option, though.

@Jed_Campbell The reason I am using PCA is really just because I understand it more. I am not sure how I would perform another analysis on such disparate types of data when the goal of what I'm doing is more to find associations. The example I gave above is more of a trimmed down version of what I am doing (151 properties of different materials), so if you have any suggestions, I'd love to hear them.

Thanks!

Mark_Bailey · Answer

I am not sure I understand. You can analyze functions (data series) with the Functional Data Explorer. Each series is a separate function. What is different in the question you asked? The PCA is on the functions.

Have you read the JMP Help about FDE? Do the examples help answer your question?

Jed_Campbell · Answer

So far I've selected certain points from those data series based on typical conditions (e.g. room temperature), but it would definitely elevate the analysis if the entire data series for each could be used.

Sounds like you're in the right spot: FDE should be able to use the entire output/shape of your data, rather than just certain points.

I see the DFPCA option in the functional data analysis platform.

Is there a reason you're using that rather than fitting a model to your data? In my experience, fitting a model (Red Triangle...Models) is usually the first step. Direct FPCA is certainly an option, though.

[Is there] a way to do multiple data points and data series, and do PCA with all of it.

Yes. If I'm understanding correctly, you'd use either the FPC Profiler or (more likely) the FDOE Profiler. The FPC Profiler shows how changes in FPCs affect the shape of the output, and the FDOE Profiler shows how changes in DOE inputs affect the shape of the output. I've put a screenshot below and attached a sample data file.

Mill DOE.jmp