Do you mean: Given two numbers x and and y drawn from a specific sample S of numbers (or a specific probability distribution D over the set of numbers)?
Without this background S or D, the question is meaningless... Given a distribution D, one can draw a sample S, of course; so the case where one has a sample S is sufficient to deal with One sensible measure would be: What ratio of the numbers in the sample S are greater than max(x,y) or less than min(x,y) , as opposed to lying between x and y? This gives you 1 if x and y are identical or have no members of S between them; and 0 if x and y are the opposite endpoints of the sample. If you want a scaling between -1 and 1 instead of 0 and 1, just linearly normalize... In OpenCog, this (but without the normalization into [-1,1]) is how we would measure similarity between two NumberNodes relative to a given QuantitativeSchemaNode, consistent with our approach of quantile normalization for predicatizing quantitative characters: http://wiki.opencog.org/w/QuantitativePredicate An advantage of ranking based approaches like these, is that they are robust with respect to the wide variety of different probability distributions one encounters in the real world... -- Ben G On Thu, Feb 20, 2014 at 1:01 PM, Piaget Modeler <[email protected]>wrote: > Hi all, > > For all you statisticians out there... > > I'm working on an algorithm for numeric similarity and would like to > crowdsource the solution. > > Given two numbers, i.e., two observations, how can I get a score between > -1 and 1 indicating their proximity. > > I think I need to compute a few things, > > 1. Compute the *mean* of the observations. > 2. Compute the standard deviation *sigma* of the observations. > 3. Compute the *z-score* of each number. > > Once I know the z-score for each number I knew where each number lies > along the normal distribution. > > After that I'm a little lost. > > Is there a notion of difference or sameness after that. > > This might help.. > > > http://www.dkv.columbia.edu/demo/medical_errors_reporting/site010708/module3/0510-similar-numeric.html > > Your thoughts are appreciated ? > > Michael Miller. > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/212726-deec6279> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org "In an insane world, the sane man must appear to be insane". -- Capt. James T. Kirk ------------------------------------------- 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
