I am thinking about doing the following to a data set with $N$ samples and $m$ features
1) Train using semi-supervised learning and cross validate on labeled data using LOO-CV to select the best model.
2) Once we have the best model, eliminate one feature and go again to 1. Search again for the best model.
3) Stop when you have $n < m$ features and the best model
Do this tend to overfit?
Edit: Would it be better if I adjust the model with all the features and then perform backward feature selection only?