You're making gross assumptions about what similarity is without leaving any wiggle room, which is fine and might work for the purposes. I just generalized the formula a particular way.
I like my formula. Michael didn't put any limits on the numbers J John From: Aaron Hosford [mailto:[email protected]] Sent: Friday, February 21, 2014 7:46 PM To: AGI Subject: Re: [agi] Numeric Similarity How would you go about efficiently estimating Kolmogorov complexity for floating point numbers? The formula f(a, b) = 1 / (1 + d(a, b)) should do the job regardless of the choice of distance metric d, so long as it conforms to the formal definition of a distance metric. It's really a matter of what dimension of similarity you want to look at. There is linear distance, d(a, b) = |a - b|, your Kolmogorov-based distance |K(a) - K(b)|, harmonic distance, d(a, b) = n * d (where n / d = |a / b| and gcd(n, d) = 1, only good for nonzero a, b), discrete distance d(a, b) = 1 if a = b and 0 otherwise, or even other definitions based on Kolmogorov complexity, like d(a, b) = K(|a - b|). I think, though, that for most applications, the simplest definition, d(a, b) = |a - b|, is going to make the most sense. On Fri, Feb 21, 2014 at 6:27 PM, <[email protected]> wrote: K() would be the Kolmogorov complexity. Matt Mahoney always complains that the K Complexity is not computable but never talks about it being estimable. John On 2014-02-21 19:05, Piaget Modeler wrote: I like this too. How would one define K ? ~PM ------------------------- From: [email protected] To: [email protected] Subject: RE: [agi] Numeric Similarity Date: Fri, 21 Feb 2014 16:18:16 -0500 It could also be something like this: Similarity(A, B) = 1 / (1 + |K'(A) - K'(B)|) where K'(A) is the estimated complexity of A. The K' function is dependent on observer formulaics and resources. John FROM: Piaget Modeler [mailto:[email protected]] SENT: Friday, February 21, 2014 3:46 PM TO: AGI SUBJECT: RE: [agi] Numeric Similarity Actually Aaron Hosford just recommended 1 / (1 + | a - b | ) Which I like much better. Thanks Aaron. ~PM ------------------------- From: [email protected] To: [email protected] Subject: RE: [agi] Numeric Similarity Date: Fri, 21 Feb 2014 06:02:46 -0800 Thanks to all respondents. In the end I found a classic numeric similarity metric: 1 - | a - b | It's not ideal since numeric scores can dominate other attribute scores. Ergo, I have to devise a good weighting scheme. Nothing's perfect I suppose. Cheers, ~ PM AGI | Archives [1] [2]| Modify [3] Your Subscription [4] AGI | Archives [1] [5]| Modify [3] Your Subscription [4] AGI | Archives [1] [2] | Modify [3] Your Subscription [4] AGI | Archives [1] [5] | Modify [6] Your Subscription [4] Links: ------ [1] https://www.listbox.com/member/archive/303/=now [2] https://www.listbox.com/member/archive/rss/303/19999924-4a978ccc [3] https://www.listbox.com/member/? <https://www.listbox.com/member/?&> & [4] http://www.listbox.com [5] https://www.listbox.com/member/archive/rss/303/248029-3b178a58 [6] https://www.listbox.com/member/? <https://www.listbox.com/member/?&;> & ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/23050605-2da819ff Modify Your Subscription: https://www.listbox.com/member/? <https://www.listbox.com/member/?&;> & Powered by Listbox: http://www.listbox.com AGI | <https://www.listbox.com/member/archive/303/=now> Archives <https://www.listbox.com/member/archive/rss/303/248029-3b178a58> | <https://www.listbox.com/member/?&;> Modify Your Subscription <http://www.listbox.com> ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
