Derek, On 7/22/08, Derek Zahn <[EMAIL PROTECTED]> wrote: > > > > Remembering that absolutely ANY function can be performed by > > passing the inputs through a suitable non-linearity, adding them > > up, and running the results through another suitable non-linearity, > > it isn't clear what the limitations of "linear" operations are > > You might be interested in "kernel PCA" > http://en.wikipedia.org/wiki/Kernel_principal_component_analysis >
Which brings to mind other issues, e.g. the need to work with the logarithms of intensities to make the same relative differences have the same impact on the result. Then, what happens to the units when you logarithmnitize the data? I suspect that what I REALLY need is to find someone who has been twiddling with PCA-related methods for the last 20 years and find out what sorts of things work and what doesn't. > > Also, once you start looking beyond pure PCA the ideas begin to blur with > the "clustering" you abhor, with things like kohonen networks, k-means > clustering, etc. I'm not a huge expert on these topics although I do think > that dimensionality reduction (for generalization/categorization if nothing > else) must be an important piece of the puzzle. These methods including PCA > are all mainstream in machine learning. > You seem to be saying much the same things as Richard. OK, let me say it back in different words to see if I got it: There are enough smart people working on this that if there were a nice solution, then it would have been found long ago. Some not-so-nice approaches have been tried but they didn't seem to produce anything valuable. If I got the above correct, then I suspect that everyone subscribes to some common falacy, e.g. if they disclaimed the falacy in a paper, then it would never get published. The falacy would be found among the solid beliefs in the field. I wonder what these are? Hmmm... > > > Did you see anything there that was not biologically plausible? > > The fact that feature maps in the early visual system don't actually seem > to detect the principal components as found in the methods of that paper. > Instead, they appear to detect things that the principal components can > also be usefully combined to represent (which are just the obvious features > of a segmented visual field). > > >> For a much more detailed, capable, and perhaps more neurally > >> plausible model of similar stuff, the work of Risto Miikkulainen's > >> group is a lot of fun. > > > > Do you have a hyperlink? > > The book I'm thinking of is _Computational Maps in the Visual Cortex_. see > http://computationalmaps.org which has enough material to get the idea. > It must be REALLY good to command a 3-digit price for even a used copy. 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
