Normalization of data is to scale the data so that it falls into a small specific interval. In some comparison and evaluation index processing, it is often used to remove the unit limitation of the data and convert it into a dimensionless pure value, which facilitates comparison and weighting of indicators of different units or magnitudes.
The most typical one is the data normalization process, that is, the data is uniformly mapped to the [0,1] interval. The common data normalization methods are:
min-max normalization
Also called dispersion standardization, it is a linear transformation of the original data, so that the result falls in the interval [0,1]. The conversion function is as follows:
Where max is the maximum value of the sample data and min is the minimum value of the sample data. One drawback of this method is that when new data is added, it may cause changes in max and min, which need to be redefined.
log function conversion
The method of log function conversion based on 10 can also be implemented. The specific method is as follows:
After reading many online introductions, x * = log10 (x) is actually problematic. This result does not necessarily fall on the interval [0,1]. It should be divided by log10 (max). The maximum value, and all data must be greater than or equal to 1.
atan function conversion
The normalization of data can also be achieved with the arc tangent function:
When using this method, it should be noted that if the interval to be mapped is [0,1], the data should be greater than or equal to 0, and the data less than 0 will be mapped to the [-1,0] interval.
Not all data normalization results are mapped to the [0,1] interval. The most common standardization method is Z standardization, which is also the most commonly used standardization method in SPSS:
z-score normalization (zero-mean normalization)
叫 Also called standard deviation standardization, the processed data conforms to the standard normal distribution, that is, the mean is 0, the standard deviation is 1, and its conversion function is:
Where μ is the mean of all sample data and σ is the standard deviation of all sample data.
