Using pca to extract singular cross-section from mixed cross-sections

I am tying to extract individual atmospheric cross-sections from a mixed cross-section made up of multiple species with pca. How do I do this and is pca the best option? I have tried pca, fastica and nnmf but all doesnt seem exactly what i want. pca outputs negative values for the principle components and then when reconstructing, each component is jus a variation of the input data rather than a unique part. ica and nnmf requires knowing the number of components before hand and again outputs negative or weird components. any help would be great

Answer 1

[Subhajyoti]

Hi @Joshua,

It is my understanding that you are trying to extract individual atmospheric cross-sections from a mixed dataset.

Clustering algorithms like 'K-Means' or 'DBSCAN' can be used to group similiar datapoints together. These methods help in identifying and categorizing the natural groupings in data, if the components are distinct enough.

An 'autoencoder' might be beneficial in dimensionality reduction or feature learning. Autoencoders can learn efficient representations of your data, which can be useful for tasks like anomaly detection or data compression. You can experiment with different neural network-based autoencoders architectures to see if they can separate the components.

Refer to the following MathWorks Documentations to know about these methods:

• Auto-encoder: https://www.mathworks.com/help/deeplearning/ref/autoencoder-class.html
• Train auto-encoder: https://www.mathworks.com/help/deeplearning/ref/trainautoencoder.html
• DBSCAN: https://www.mathworks.com/help/stats/dbscan.html
• K-Means: https://www.mathworks.com/help/stats/kmeans.html
• Cluster data: https://www.mathworks.com/help/stats/clusterdata.html

[Joshua]

Hi @subhajyoti,

Thanks for your help and your comment. Much appreciated.

I don’t think I can use clustering methods as the input are spectra-like data with n observations of arrays each containing a polygon/curve. These arrays contain very similar data but for example 1 observation might have a peak at 200 where another will have a peak at 300. So trying to find the common/most common elements to say “okay at this width and this height there is cross-section a then over here is cross-section b and c which make up the input data”. I also don’t know the number of components/sub-parts/individual cross-section. It’s a bit like finding the pieces of an already complete jigsaw puzzle. Does that make sense? I can attach an example.