Abram, On 7/23/08, Abram Demski <[EMAIL PROTECTED]> wrote: > > The Wikipedia article on PCA cites papers that show K-means clustering > and PCA to be in a certain sense equivalent-- from what I read so far, > the idea is that clustering is simply extracting discrete versions of > the continuous variables that PCA extracts. > > > http://en.wikipedia.org/wiki/Principal_component_analysis#Relation_to_K-means_clustering > > Does that settle it?
Sorry for the delay, but I have been working on a response to this. 1. That the article that makes this point was first presented in 2004 makes my original point that despite the advanced age of PCA, that there are some really new and exciting advances taking place, not withstanding the many comments here to the contrary, apparently by people who have NOT been keeping up on this re-emerging field. 2. Both clustering and PCA methods presume that data is collected, analyzed, and some sort of decision is made. However, unless the neurobiological and CS worlds have missed something really important (it sure wouldn't be the first time), neurons probably do this incrementally, though there ARE other viable possibilities, e.g. that groups of neurons could work together to develop the principle component transformations or something similar, during which time their output would indicate nothing of value. If the underlying incremental presumption is true (wouldn't sound math suggest it to be false?!), then a sort of "derivative" with respect to time of PCA or K-means must be developed, to show how neurons should change second-by-second as they learn. More fun with matrix algebra. 3. OK, I seem to be right back where I started - still looking for someone who lives and breathes matrix math, and yet still speaks enough English for us mere mortals to be able to communicate with. The problem (as I see it) is one of perverse notation and/or orthogonal complexity, where people manipulate matrix operators without really relating to what is happening underneath. Only this way could K-means remain separate from PCA for so long. Where is the idiot savant who could transform this field? So, in answer to your question, no, it is NOT settled, though this may move it to the next chapter in its development. Perhaps my predicted coming CS "Theory of Everything" needs a more descriptive title, but I still see it just sitting there waiting for some matrix math gurus to unravel and publish (in plain English) the methods to converge the now disparate fields of AI, NN, Compression, and Encryption. Steve Richfield ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=108809214-a0d121 Powered by Listbox: http://www.listbox.com
