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Problem description：I'm working on a machine learning project, and one of the features is represented by the proportion of three levels' sample numbers. When I was doing preprocessing normalization, I can't find a suitable method to normalize the proportion. I would like to ask everyone that if there are suitable ways to normalize the proportion.

My ideas:My current ideas are to convert the proportion into a number, or to get a number by comparing the proportion,such as comparing 1:2:3 with 1:1:1, so that it can be normalized, but I have not found a suitable method on the Internet, I hope to receive your suggestions. Thank you!

kangkang_1024
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1 Answers1

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I think the answer depends on what you want to achieve by normalization. If you have three value $\{ a,b,c \}$ then there are several ways of normalizing them, including the following

  • To normalize so that their sum is $0$ but their differences remain the same, subtract $\frac{a+b+c} 3$ from each value.
  • To normalize so that their sum is $1$ and they retain the same proportions, divide each value by $a+b+c$.
  • To normalize so that the sum of their squares is $1$ (i.e. so that $(a,b,c)$ becomes a unit vector), divide each value by $\sqrt{a^2+b^2+c^2}$
gandalf61
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  • Thank you for your answer ! Maybe I didn't describe it clearly.The way I extract this feature is to define three levels,then get the proportion of three levels as a feature.So my feature vector is like"1:2:3,1:3:4,1:1:1...",so the way you suggest cannot work. How to describe or quantify these proportions is what I puzzled.Hope to get your suggestions. – kangkang_1024 May 26 '20 at 11:49
  • @kangkang_1024 I am still not clear what you are trying to achieve. My best guess is you want to reduce each feature vector to a single value so that you can compare two feature vectors. If so, is $(1,1,1)$ better than, the same as, or worse than $(2,2,2)$ ? Is $(1,2,3)$ better than, the same as or worse than $(1,3,2)$ ? If the feature vectors had two co-ordinates instead of three, would the problem be simpler ? To get any useful answers, you need to describe your problem in more detail. – gandalf61 May 26 '20 at 14:04
  • I’m working on image-based ship target recognition, I am studying the relationship between data distribution and recognition accuracy. The data distribution here refers to the number distribution of different attributes in the dataset, such as the proporation of the number of military ships and civilian ships,for example 1: 2. – kangkang_1024 May 26 '20 at 14:56
  • But if the attribute has three levels, then 1: 2: 3 will occur. For example, if I divide the image target scale into three categories, large target, medium target, and small target, then the data distribution of the target scale is the [large target: medium target: small target], so 1: 1: 1 and 2: 2: 2 are same, but 1: 2: 3 and 1: 3: 2 are different. – kangkang_1024 May 26 '20 at 14:56
  • I want to find a way to represent the distribution of these three terms, so that I can use some statistical or machine learning methods for further analysis. My idea is to quantify them into a number, or compare it with a uniformly distributed 1: 1: 1 to get a value, but there is no better way. Thanks for your patience. – kangkang_1024 May 26 '20 at 14:56
  • I'm new here, if there is any inappropriate behavior, I hope to get your forgiveness. – kangkang_1024 May 26 '20 at 14:59