When according to various indicators to get comprehensive index, due to the different contribution of each index composite indicator, the corresponding weight should be different, a large contribution to the overall index index is more important, it should assign more weight. How to determine the weight of each index, presented here in two ways: pca and entropy method to determine the weight. Engineering can also be used in determining characteristic feature weights.
First, the entropy method
1, the concept of entropy
In information theory, entropy is a measure of the uncertainty of a random variable. Entropy value, the smaller the degree of disorder, uncertainty, the larger the amount of information; the higher the entropy, the greater the degree of disorder, the greater the uncertainty, the smaller the amount of information. Available entropy value is calculated degree of dispersion characteristics, a large degree of dispersion characteristics greater impact on the overall value.
Entropy large and small amount of information, the weight should be small; small entropy, informative, weight should be large.
Entropy is calculated
2, entropy method to determine the weights
| Indicator 1 | Indicator 2 | …… | Index m |
| ... | ... | ... | ... |
1 to determine the index weight index weight m
Number of occurrences of the different values of the index value difference between large and small entropy, informative, weight should be large; number of occurrences of the different values of the index value difference between small and large entropy, a small amount of information, the weight should be small.
When the index values are identical m, maximum entropy, the indicator may be removed.
The step of determining the weight entropy method:
1, normalized
On the index value is normalized, when normalized, it should consider the impact indicators
When the index value is the better, using equation
x=(x-xmin)/(xmax-xmin)
When the index value is as small as possible, using the formula
x=(xmax-x)/(xmax-xmin)
2, the definition of entropy
indexes m, n is an evaluation target
I-indexes
3, the definition of entropy
Two, pca determine the weight
pca dimensionality reduction is a method of unsupervised, pca by linear transformation of the original may be associated vectors into n linearly independent k-dimensional vector. With a weighting factor to determine the weight pca you need to know three conditions:
- Index coefficient in the linear combination of the principal components
- Variance contribution rate of the main components
- Index weight normalization
ex: n principal components, m indexes
w represents a main component of each coefficient, w ij of coefficients representing the first principal component a j-th index, F I denotes a first variance contribution of the principal component
The right of the q indexes of weight
Normalized
