I don’t believe your statement is globally true. However, it sounds like you’re saying something about principal compliment analysis (PCA) in which clustering is often done by reducing complex (high dimensional) data sets into more simple sets by recovering the principal axes along the vector of the greatest variance in the data set.
Yes I think so. I was able to recognize what you were asking right away and I provided a specific example of how that concept is used with spatial data in my field. We also use PCA extensively in image analysis to look for anaomalies and reduce noise. Since PCA projected data is projected along the line of the data variance, a point that lies at the extreme far end is less similar to the mean point value compared to a point on the low end of the axis. In this case, we are looking at spectral variance rather than spatial variance in finding anomalous materials 😉
You see how you can draw a (slanted) line through those dots and they’re all mostly along that line, very close to it?
The line would represent things that are directly proportional, which would be “very similar” to each other.
Whereas if you go outwards from the line (“in the direction of high variance”), then those dots would have “no relationship” to the line, would not “follow” the proportionality etc.
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