variable importance in projection 计算公式
There isn't a single specific formula to calculate variable importance in projection, as it depends on the specific projection technique being used. However, one commonly used approach is to measure the decrease in the accuracy or error of the projection model when a variable is excluded or their values are randomized.
One such method is the mean decrease accuracy or mean decrease impurity, which is calculated as follows:
1. Train a projection model on the entire dataset and record its accuracy (or error) as a baseline.
2. For each variable, randomly permute its values (shuffle them randomly) in the dataset, while keeping all other variables unchanged.
3. Retrain the projection model on the permuted dataset and record the new accuracy or error.
4. Calculate the decrease in accuracy or increase in error compared to the baseline for each variable.
5. Repeat steps 2-4 multiple times (e.g., with different random permutations) to obtain an average decrease in accuracy or increase in error for each variable.
Variables that cause the largest decrease in accuracy or increase in error when permuted are considered to have higher importance in the projection model.
Different projection techniques may have variations of this formula or entirely different methods to calculate variable importance. It is recommended to consult the specific documentation or research papers related to the projection technique you are using to find the appropriate formula for variable importance in that context.variable used in lambda

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