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I'm predicting ozone concentration based on meteorological and seasonal variables. In the feature engineering stage I converted the MONTH, DAY_OF_WEEK, DAY_OF_YEAR to its sin and cosine components because I read in some articles that this is how circular values should be treated.

I have 3 questions regarding this:

1) When I try to do feature selection, or feature importance, why is the cosine having more importance than sine for the same variable? Is there a scientific explanation?

2) I'm trying to study which variables have higher importance for predicting ozone, but how can I determine that since the seasonal variables are split into sine and cosine?

3) In the feature selection, can I drop the sine of the same variable and keep the cosine if the cosine has more importance/weight while the sine isn't?

For example, here is the feature importance by XGBoost Regressor:

enter image description here

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  • $\begingroup$ Like on an actual clock, think about what cosine tells you what time it is (is it day time or summer time? ) and maybe you can hypothesize about that time's influence on ozone $\endgroup$
    – Drey
    Aug 7, 2019 at 21:05
  • $\begingroup$ Is discarding the sine logical that when I try to do feature selection? I'm really stuck at this. $\endgroup$
    – M. Grimm
    Aug 8, 2019 at 9:28
  • $\begingroup$ Depends on what you need the signal for. If you need it for reconstruction when predicting stuff and you want to explain it then don't discard it. If you only want to predict and your prediction metric is sufficiently presice then you may discard it. $\endgroup$
    – Drey
    Aug 8, 2019 at 9:36
  • $\begingroup$ Can you please tell me what do you mean by 'reconstruction'? do you mean having to explain the most important features for predicting the output or so? $\endgroup$
    – M. Grimm
    Aug 8, 2019 at 12:20
  • $\begingroup$ Not the features. But to explain the actual reasons why the prediction is the way it is. For example, if you want to explain in which "month" your prediction computes your values you will inevitably need the sine component (see your point 2). You can do what you mentioned in 3) if you don't need to explain what natural phenomenons support your prediction. And 3) is a hint that some months (the ones with high cosine value) are more important for ozone prediction than others. $\endgroup$
    – Drey
    Aug 8, 2019 at 14:40

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