How to Normalize Indicators: 7 Essential Dimensionless Transformation Methods
This article explains the concept of indicator dimensionless processing and introduces seven common transformation techniques—including standard sample, ratio, vector normalization, range, and efficacy coefficient methods—to convert raw indicator values into comparable evaluation scores.
1 Dimensionless Processing of Indicators
Dimensionless processing, also called indicator normalization, uses mathematical transformations to eliminate the influence of units and magnitude of original indicators.
Thus, there are actual values and evaluation values. The value after dimensionless processing is called the indicator evaluation value.
The dimensionless process converts actual values to evaluation values.
For multiple evaluation objects, each object has several indicators with observed values (formulas omitted).
Below are several common indicator transformation methods.
2 Standard Sample Transformation
Let the sample mean and sample standard deviation be used to obtain the standardized observation value (formula omitted).
3 Ratio Transformation
For extremely large indicators, set a transformation (formula omitted). For extremely small indicators, set a transformation (formula omitted). This method preserves proportionality of values before and after transformation, though not all transformed values may appear simultaneously.
4 Vector Normalization
For extremely large indicators, set a transformation (formula omitted). For extremely small indicators, set a transformation (formula omitted).
5 Range Transformation
For extremely large indicators, apply a range transformation (formula omitted). For extremely small indicators, apply a range transformation (formula omitted). After transformation, all indicators have a maximum and minimum; the optimal indicator value is the maximum, and the worst is the minimum. The drawback is that values are not proportional before and after transformation.
6 Efficacy Coefficient Method
The coefficients are fixed constants representing a "translation amount" (baseline value) and a "rotation amount" (scaling factor).
7 Summary
This article introduced several common data dimensionless processing methods (standard transformation, ratio transformation, range transformation, vector normalization, and efficacy coefficient method).
References
ThomsonRen https://github.com/ThomsonRen/mathmodels
司守奎，孙玺菁 Python数学实验与建模
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