As mentioned in the previous post I will write a bit about the random feature selection in random forest. In the training step at each split in a random forest k features are selected at random from all features. For these features the ideal split according to a split criteria is chosen and the feature which performs best under all features is chosen as feature. The number k should not be set too high, so that not always the same features are chosen, but also not too small, so that at least some relevant features come into the comparison. It also depends highly on the dataset. If in the dataset there are only few features with relevance, the number k should be set sufficiently high, and vice versa.

The introduction of randomness in the feature selection process seems to be advantageous in many cases. The default in many packages like randomForest is to choose k as the square root of the number features.