How does feature selection impact outlier detection and also, removing outliers impact feature selection? It could be a basic question. However, just to know the boundaries, I asked. Thanks in advance. I have gone through the following:Feature selection and outlier order
Outlier detection is part of data preprocessing and used to remove some of the rare events but it could happen that rare events are important to us like fraud detection in that case it becomes important and so we can't do outlier detection beforehand.
In that case we do various approaches like undersampling of majority events or oversampling of minority class. For various approaches refer this
You could also look into KPCA. Having said that there is no particular solution it all depends upon your dataset.