I've come across a scenario where I have 10 signals/person for 10 people (so 100 samples) containing 14000 data points (dimensions) that I need to pass to a classifier. I would like to reduce the dimensionality of this data and PCA seems to be the way to do so. However, I've only been able to find examples of PCA where the number of samples is greater than the number of dimensions. I'm using a PCA application that finds the PCs using SVD. When I pass it my 100x14000 dataset there are 101 PCs returned so the vast majority of dimensions are obviously ignored. The program indicates the first 6 PCs contain 90% of the variance.
Is it a reasonable assumption that these 101 PCs contain essentially all the variance and the remaining dimensions are neglectable?
One of the papers I've read claims that, using a similar (though slightly lower quality) dataset than my own, they were able to reduce 4500 dimensions down to 80 retaining 96% of the original information. The paper hand-waves over the details of the PCA technique used, only 3100 samples were available, and I have reason to believe less samples than that were used to actually perform PCA (to remove bias from the classification phase).
Am I missing something or is this really the way that PCA is used with high dimensionality-low sample size dataset? Any feedback would be greatly appreciated.