Evaluation - grey correlation analysis

1、 effect

For the factors between the two systems , A measure of the magnitude of its relevance over time or different objects , It's called relevance . In the process of system development , If the change trend of the two factors is consistent , I.e. high degree of synchronous change , It can be said that the two are highly related ; conversely , Lower . therefore , Grey correlation analysis refers to the quantitative description and comparison of the development and change of a system , Its basic idea is to judge whether the relation is close by determining the geometric similarity between the reference data column and several comparison data columns , It reflects the degree of correlation between curves .

2、 Input / output description

Input : The characteristic sequence is at least two or more quantitative variables , The mother sequence （ Related objects ） by 1 Quantitative variables .
Output : Reflect the correlation degree between the assessment indicator and the parent sequence .

3、 Case example

Analysis of recent 10 During the year , Number of cinemas , Number of viewers , Attendance rate , The fare 、 The influence of factors such as the number of films on the box office of the whole year . The movie box office is the parent sequence , Number of cinemas , Number of viewers , Attendance rate , The fare 、 Factors such as the number of films online are characteristic sequences .

4、 Modeling steps

1. Determine the characteristic sequence and the parent sequence
The comparison sequence is

The mother sequence ( That is, evaluation criteria ) by

2. Dimensional unification of index data

In order to truly reflect the actual situation , Exclude the influence caused by the difference of each index unit and the great difference between the numerical orders of magnitude ring , Avoid unreasonable phenomena , It is necessary to unify the dimensions of the indicators . First, calculate the average value of each indicator column , Then divide each element of the indicator column by the average value of the indicator column .

3. Calculate the correlation coefficient

Calculate each comparison sequence and Reference sequence pair The correlation coefficient of the corresponding element ：

Is the resolution coefficient , stay (0,1) The inner value is , The smaller the resolution coefficient , The greater the difference between correlation coefficients , The more discriminative , Usually take 0.5.

4. Calculate correlation order
Calculate the weighted average value of the correlation coefficient between each index and the corresponding element of the reference sequence , To reflect the relationship between each control device object and the reference sequence , And call it the degree of relevance , Write it down as

5. Analyze the calculation results

According to the size of grey weighted correlation degree , Establish the correlation order of each evaluation object . The more relevant , It shows that the more important the evaluation object is to the evaluation standard .