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using the sigmoid-function to take large numbers and make them manegable in php

Sometimes - if you have large databases/sites - you can end up dealing with large numbers to handle

Let's say you are YouTube and need to order a serch reslut with 25,000,000 results and you want to order them by number of views and upvotes and... to get a relevance score - but then you have a couple of PewdePIe videos with 50,000,000 views and 2,000,000 upvotes and soon your numbers becomes a 'little big'
...

luckily some smart people have decided to help you and have designed some mathematical functions to reduce those large numbers down to size

one such function is the sigmoid function:
S(x) = 1/(1+exp(-x))
which greatly reduces the size of your numbers - but in php it only really works for numbers between about -700 and +32 - anything below will just return 0 and anything above will just return 1... so not much help after all

so here's a little script that'll greatly increase the range of usable numbers by simply adding log10 to x in the expression the number range increases greatly - but now you can't 'srink' negative numbers

well here is a little function to fix that (feel fre to use if needed)

PHP Code:
function sigmoid_log10($x) {
    if ($x<0) {
        return -(1/(1+exp(-log10(abs($x)))));
    } else {
        return 1/(1+exp(-log10($x)));
    }
} 
Now you can take any number between -10xE32 and +10xE32 - and with an acuracy of 10xE-32 reduce it to a usable value between -1 and +1

And you can even use it in MYSQL directly:

PHP Code:
// use count(0) to get the values you want to use in your relevance-score
SELECT 
    // select the values you need for your relevance score
    ( SELECT COUNT(0) FROM videovote AS vvup WHERE vvup.videoID = /* something */ AND vvup.upVote IS NOT NULL ) AS upvote,
    ( SELECT COUNT(0) FROM videovote AS vvdown WHERE vvdown.videoID = /* something */ AND vvdown.downVote IS NOT NULL ) AS downvote,
    ( SELECT COUNT(0) FROM ... // you get the drill,
    
    // and then use the values you collected above and put it into the modified sigmoid function
    ( 1 / ( 1 + EXP ( -LOG10 ( /* here goes your values to be scored for relevance */ ) ) ) ) AS score
    
    // and then just order by score
    ORDER BY score
    
    // example of a what's hot video score computation using this - but you can make your own collectiong the values you want and putting them into the formula above
    ( 1 / ( 1 + EXP ( -LOG10 ( ( LOG10 ( ABS ( upvote- downvote) + 1 ) * SIGN ( upvote- downvote) + LOG10 ( views + 1 ) + LOG10 ( IdeaCount + 1 ) + ( UNIX_TIMESTAMP ( v.date ) / 600000 ) ) ) ) ) ) AS score 
Feel free to use at your risk (as with great power comes great responsibility) :)

برچسب: نویسنده: آیلین رضوانی تاريخ: دوشنبه 27 آذر 1396 ساعت: 7:55

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