in reply to [OT] Normalizing the return result of an exponential formula

I would like to change the formula to make the upper limit of the range dependent only on importance and not on radius.

Why not just omit the radius from the equation?

That way, the 'boost' become dependant upon just the distance from the perimeter of the circle regardless of the circles size: 

sub x{ 
    my( $i, $r, $d, $o ) = @_; 
    return $i / $d**$o; 
}

print x( 100, 0, $_, 0.5 ) for map 2**$_, 4..13;;
25
17.6776695296637
12.5
8.83883476483184
6.25
4.41941738241592
3.125
2.20970869120796
1.5625
1.10485434560398

print x( 100, 1000, $_, 0.5 ) for map 2**$_, 4..13;;
25
17.6776695296637
12.5
8.83883476483184
6.25
4.41941738241592
3.125
2.20970869120796
1.5625
1.10485434560398

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Re^2: [OT] Normalizing the return result of an exponential formula
by clinton (Priest) on Apr 14, 2011 at 16:55 UTC

    What I was trying to achieve with radius was to give the user the ability to say: "anything within this circle is really important", where that circle might be a country, or a province. So the curve might look like:

    
    16   : @@@@@@@@@@@@@@@@@@@@@@@@@  -
    32   : @@@@@@@@@@@@@@@@@@@@@@@@  | inside radius
    64   : @@@@@@@@@@@@@@@@@@@@@@     -
    128  : @@@@@@@@@@@@@@             
    256  : @@@@@@@@@@                
    512  : @@@@@@                    
    1024 : @@@                        
    2048 : @@
    4096 : @
    8192 : @

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[d/l]

      Then I misunderstand what you meant by "2. radius: ie any distance within this inner radius should be pretty much as important as any other point within this radius"

      To me that reads as, everything inside the circle is equally important, but as the distance outside that circle increases, the importance falls off exponentially. This was reinforced by your adding the distance to the radius in your formula.

      As that does not appear to be the case, and as you new diagram does nothing to explain the relationship between 'radius' and 'distance', I think you are going to have to explain the relationships between the 4 input variables much more clearly?

      For at least me. I'm sometimes quite good at reading between the lines, but with your latest information I cannot reconcile your formula, terminology, and stated goals.Ie.

      Is 'distance' measured inside the circle? From the centre toward the edge? Or from the edge toward the centre?

      Is 'boost' an exponential decline in 'importance' over 'distance'? As suggested by the term 'dropoff'. (It is a strange name for a decline in anything?)

      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]

        Apologies, I'm not expressing myself terribly well. Let me explain what I'm ACTUALLY trying to achieve, and perhaps the solution will be more apparent.

        I am building an autocomplete function of place names:

        1. Places could be districts, towns, cities, regions, countries.
        2. Each place has a "rank" eg a capital is more important than a village
        3. Each place also has a lat/long position
        4. Each place is indexed in ElasticSearch (a lucene based full text search engine) using edge-ngrams

        Currently, to find a list of relevant place names to return, I do a search against ElasticSearch (ES) based on the text a user has typed in. ES calculates a score based on the frequency of those ngrams, with the usual full-text-search relevance scoring. I then incorporate the "rank" (eg capital vs village) into that final score and sort the results using this final score.

        I would like to add a geo-location element. So villages (low rank) close to (eg) your home town would score more highly than a city (high rank) 2000km away.

        And I would like to be able to say that eg anything with 10km, or 100km or $x km (ie it should be configurable) is more relevant than it would be by just following the curve of the formula

        But the value that gets returned (the boost) should range from (eg 0..10), so that the user of my module wouldn't have to guess about how much effect the value that they pass in might have on the results.

        It may be that I'm over thinking this.

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[d/l]

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