I am doing Principle Component Analysis of my proteomics data.
There are two groups, one is healthy control and the other one is patients.
Originally I have 90 biomarkers, and after feeding all the 90 biomarkers for PCA analysis, I have PC1 (23.3%) and PC2 (19.2%).
Then I reduced biomarkers to 23, which I did t-test and found the 23 biomarkers are significanly different between control and patients.
Then after feeding only the 23 biomarkers for PCA analysis, I have PC1 (39.3%) and PC2 (27.9%).
Now my question is, how should I interprate the results?
In the first time, PC1+PC2 is 42.5%; when I reduce the number of biomarkers, PC1+PC2 is 67.2%, so can I draw the conclusion that the two groups are clustered better in the second time than in the first time?
Or, are there any specific number that we could refer to evaluate the quality of a PCA?
Okay. So many things to talk about here.
1. Applying Student's T-Test will cut off the irrelevant features from your dataset. So, in that case, your data is more less corrupted and hence easy to hold. For example, if you've a feature that will contradict to itself (showing no relation), then preserving the information of that feature. Hence, PCA-1+PCA-2 provides better total variance after applying feature selection because now it's easy for PCA to preserve the information of the dataset as the dataset is less corrupted.
2. PCA doesn't assure better clustering. It only focusses on preserving the original data in another basis. It only reduces the data, we can't say if PCA will make the clusters better or worse but surely it'll help to reduce the dimension.
3. The way to evaluate if the FS+PCA (FS=Feature Selection) is better than PCA is to apply clustering method on both of the output data. Take PCA1 & PCA2 for both cases and cluster the data. Then measure the quality of the clusters and come to a conclusion which one works better.
From my experience, I can predict that FS+PCA will provide a better cluster. But as there's no literature which proves the statement (it's only experimental assumption not law/theory), experimenting is the best option.
You don't say anything about the factor loadings, but presumably you deleted the biomarkers that had the lowest loadings, so then your structure for the 23 case would be cleaner (clustered better) because you retained the biomarkers that produced the best structure, i.e., had a high loading on only one of the two PCs.
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