Interesting. Examples are in spaces where you can count dimensions (colour, size,..). Be interesting if some are fractional.
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You mean 0.5 dimension, for example?
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Yes. Fractal.
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I'm not sure but given all the noise I am sure it does give output that's a real number. But I am no expert!
@ProfData can explain more, I am sure. -
I did read the whole paper, with interest. Looks like really useful ideas so look forward to seeing it used more. Thanks for the link.
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You're way ahead of me, I have not read the whole thing yet!
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I wonder what dimensionality of c elegans nervous system is
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given an input or like the max it can cope with?
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asking me that question has made me think pretty hard about what a meaningful estimate would mean so... not sure!
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In the preprint or just in terms of an organism without a brain?
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IMO, unless you have really good data or really know what the noise structure is, trying to quantify "true underlying dimensionality" is a bit of a pointless exercise.
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Not to say that one can't quantify dimensionality in practical ways that give insight into the patterns of the data, but I'm wary of claims re: the "truth". (i.e. we're all just looking at shadows on Plato's cave)
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Yeah, no magic solutions, but one can find best model, which can be illuminating. E.g., dimensionality difference dependent on task.
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Completely agree! I think there's probably some interesting work on dimensionality collapse prior to critical transitions, as well.
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