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[D] Confused with axis and space

If i apply the dirichlet process, or any other clustering method for that matter, am able to create components/clusters out of my data, these are plotted on a 2d plane. What are the axis that define this space? What are the plots and clusters defined as? And why is it safe to assume that the distance between each value can determind whether or not the data shares a similar structure / topic?

submitted by /u/Unlistedd
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