[AI practice] data normalization and standardization of machine learning data processing

Data normalization for machine learning data processing 、 Standardization

This paper introduces three normalization methods 、 Standardized methods .

1.min-max Standardization (Min-max normalization)

Linear transformation of the original data , Make the result fall to [0,1] Section , The conversion function is as follows ：
$$x^{\ast }=\frac{x-min}{max-min}$$

• matters needing attention
  max,min Must be fixed

2.z-score( Standard deviation ) Standardization

The mean value of the original data （mean） And standard deviation （standard deviation） Standardize data .

The processed data conform to the standard normal distribution , That is, the mean value is 0, The standard deviation is 1, The transformation function is ：
$$x^{\ast }=\frac{x-\mu }{\sigma }$$
among μ Is the mean of all sample data ,σ Is the standard deviation of all sample data .

3.nonlinearity( nonlinear ) normalization

The nonlinear normalization method is often used in Scenarios with large data differentiation , Some values are very large , Some are very small . Through some mathematical functions , Mapping the original values .

The method includes log, tangent etc. , According to the distribution of data , The curve that determines the nonlinear function ：

• Logarithmic function transformation method
  such as $y=ln(x)$, The corresponding normalization method is ：
  $$x^{\ast }=\frac{ln(x)}{ln(max)}$$
  among $max$ Represents the maximum value of the sample data ,$x^{\ast }$ Is the normalized value ,$x$ For input value , And all sample data must be greater than or equal to 1.

• Arctangent function transformation method
  The data can be normalized by using the arctangent function , namely
  $$x^{\ast }=arctan(x)\ast (2/pi)$$
  When using this method, it should be noted that if the interval to be mapped is [0,1], Then the data should be greater than or equal to 0, Less than 0 The data to be mapped to [－1,0] On interval .

• L2 Norm normalization method
  L2 Norm normalization is that each element of the eigenvector is divided by the vector L2 norm ：
  $$x_i^{\ast }=\frac{x_i}{norm(x)}$$
  among , vector $x(x_1,x_2,...,x_n)$ Of L2 The norm is defined as ：
  $$norm(x)=\sqrt{x_1^2+x_2^2+...+x_1^n}$$
  characteristic ： Converted data $x^{\ast }$ The sum of squares is 1