javascript - How do I properly normalize very large numbers algorithmic ally to a relatively small range of numbers? - Stack Ove

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I'm trying to find a way to adjust the pitch of tones based on custom user data imported from excel.

self.changePitch(30 + (parseInt(self.infoCollection.collection[j].array[i])-200/(3600)));

The above code works for "normal values" up to about 5,000. However, I want to normalize them to always fall between a minimum and maximum frequency. (200 and 3800)

I've tried using the equation found here: Which says to use (x-minval)/(maxval-minval) However, this doesn't work for all cases. When using very large numbers. IE 50 million it will still exceed the maximum frequency.

I'm trying to find a way that this will normalize any rational number up to the hundreds of millions.

Edit: Sorry for the confusion. I'm making an app that plays sound based on data placed on a graph. The purpose is to allow users with visual impairments to better understand the data using sound to get values that are relative to each other. My problem is that humans can't hear frequencies above a certain number so if there are values above 5000 or so, the app won't play any sound for that number.

Example: Profits from pany A were $200 and pany B were $50 million. The users would hear a sound for pany A, but not pany B because the frequency would be out of human hearing range.

I'm trying to find a way to adjust the pitch of tones based on custom user data imported from excel.

self.changePitch(30 + (parseInt(self.infoCollection.collection[j].array[i])-200/(3600)));

The above code works for "normal values" up to about 5,000. However, I want to normalize them to always fall between a minimum and maximum frequency. (200 and 3800)

I've tried using the equation found here: https://stats.stackexchange./questions/70801/how-to-normalize-data-to-0-1-range Which says to use (x-minval)/(maxval-minval) However, this doesn't work for all cases. When using very large numbers. IE 50 million it will still exceed the maximum frequency.

I'm trying to find a way that this will normalize any rational number up to the hundreds of millions.

Edit: Sorry for the confusion. I'm making an app that plays sound based on data placed on a graph. The purpose is to allow users with visual impairments to better understand the data using sound to get values that are relative to each other. My problem is that humans can't hear frequencies above a certain number so if there are values above 5000 or so, the app won't play any sound for that number.

Example: Profits from pany A were $200 and pany B were $50 million. The users would hear a sound for pany A, but not pany B because the frequency would be out of human hearing range.

• javascript
• normalization

Share Improve this question Follow edited Apr 13, 2017 at 12:44 CommunityBot 111 silver badge asked Feb 28, 2017 at 21:20 RemixtRemixt 59777 silver badges3030 bronze badges 9

• Can you give an example where that simple ratio formula doesn't work? It's mathematically accurate. – Pointy Commented Feb 28, 2017 at 21:22
• 1 50,000,000/3800 > 3800 – Remixt Commented Feb 28, 2017 at 21:22
• What you need to do is determine where the input value lies in the possible range of inputs, and then map that into the target domain. – Pointy Commented Feb 28, 2017 at 21:23
• 1 That makes no sense. What is the actual range of input values, and the actual target domain? – Pointy Commented Feb 28, 2017 at 21:24
• 1 I think you mix the last part of the formula. It's not max and min val of desired range but the min/max of the actual data range. So if your data has minimum value, say 200, and maximum 50,000,000, the formula is plugged this way: (valueToNomalize - 200) / (50,000,000 - 200). Then take that value, which is now normalized and scale it desired range: normValue * (maxDVal - minDVal) + minDVal – user1693593 Commented Feb 28, 2017 at 21:38

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2 Answers 2

Sorted by: Reset to default 8

The function below will perform linear normalization (thanks S McCrohan) and you can pass it the values you'll need.

https://jsfiddle/7cn57wnd/

function normalize(enteredValue, minEntry, maxEntry, normalizedMin, normalizedMax) {

    var mx = (enteredValue-minEntry)/(maxEntry-minEntry);
    var preshiftNormalized = mx*(normalizedMax-normalizedMin);
    var shiftedNormalized = preshiftNormalized + normalizedMin;

    return shiftedNormalized;

}

//Acceptable values: 0 - 10,000,000
//User enters: 99,000,000
//Normalization window: 200 - 3800

normalize(99000000, 0, 100000000, 200, 3800);

//Returns 3764

The right way to normalize this data is going to depend a lot on the distribution of values in your dataset.

For instance, if 99% of your values are in the range 0-1000, and the remaining 1% are outliers out around 10000000, then linear normalization (as in Santi's answer) will absolutely pull your data into the desired range, but it will also have that 99% normalized to values that are so close together you won't be able to hear the difference.

If you have a heavily skewed distribution like that, you're going to want to either discard the outliers, or use non-linear normalization (for instance, logarithmic). It really depends on the data and what differences you want to highlight.

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